[{"data":1,"prerenderedAt":4770},["ShallowReactive",2],{"post-\u002Fblog\u002Fkvadratni-rivnyannya-dyskryminant":3,"post-rel-\u002Fblog\u002Fkvadratni-rivnyannya-dyskryminant":4765},{"id":4,"title":5,"body":6,"date":4747,"description":4748,"draft":4749,"extension":4750,"grade":4751,"image":4752,"meta":4753,"navigation":4754,"path":4755,"rawbody":4756,"seo":4757,"stem":4758,"subject":23,"tags":4759,"topic":4763,"updated":4752,"__hash__":4764},"blog\u002Fblog\u002Fkvadratni-rivnyannya-dyskryminant.md","Квадратні рівняння, 8 клас: пояснення через дискримінант і приклади",{"type":7,"value":8,"toc":4736},"minimark",[9,297,704,707,876,936,939,944,1242,1480,1859,2378,2382,2661,2830,2948,2952,3211,3215,3381,3434,3591,3647,3651,4234,4238,4377],[10,11,12,13,196,197,291,292,296],"p",{},"Квадратне рівняння має вигляд ",[14,15,18,71],"span",{"className":16},[17],"katex",[14,19,22],{"className":20},[21],"katex-mathml",[23,24,26],"math",{"xmlns":25},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[27,28,29,66],"semantics",{},[30,31,32,36,46,50,53,55,57,60,63],"mrow",{},[33,34,35],"mi",{},"a",[37,38,39,42],"msup",{},[33,40,41],{},"x",[43,44,45],"mn",{},"2",[47,48,49],"mo",{},"+",[33,51,52],{},"b",[33,54,41],{},[47,56,49],{},[33,58,59],{},"c",[47,61,62],{},"=",[43,64,65],{},"0",[67,68,70],"annotation",{"encoding":69},"application\u002Fx-tex","ax^2 + bx + c = 0",[14,72,76,143,165,186],{"className":73,"ariaHidden":75},[74],"katex-html","true",[14,77,80,85,90,131,136,140],{"className":78},[79],"base",[14,81],{"className":82,"style":84},[83],"strut","height:0.8974em;vertical-align:-0.0833em;",[14,86,35],{"className":87},[88,89],"mord","mathnormal",[14,91,93,96],{"className":92},[88],[14,94,41],{"className":95},[88,89],[14,97,100],{"className":98},[99],"msupsub",[14,101,104],{"className":102},[103],"vlist-t",[14,105,108],{"className":106},[107],"vlist-r",[14,109,113],{"className":110,"style":112},[111],"vlist","height:0.8141em;",[14,114,116,121],{"style":115},"top:-3.063em;margin-right:0.05em;",[14,117],{"className":118,"style":120},[119],"pstrut","height:2.7em;",[14,122,128],{"className":123},[124,125,126,127],"sizing","reset-size6","size3","mtight",[14,129,45],{"className":130},[88,127],[14,132],{"className":133,"style":135},[134],"mspace","margin-right:0.2222em;",[14,137,49],{"className":138},[139],"mbin",[14,141],{"className":142,"style":135},[134],[14,144,146,150,153,156,159,162],{"className":145},[79],[14,147],{"className":148,"style":149},[83],"height:0.7778em;vertical-align:-0.0833em;",[14,151,52],{"className":152},[88,89],[14,154,41],{"className":155},[88,89],[14,157],{"className":158,"style":135},[134],[14,160,49],{"className":161},[139],[14,163],{"className":164,"style":135},[134],[14,166,168,172,175,179,183],{"className":167},[79],[14,169],{"className":170,"style":171},[83],"height:0.4306em;",[14,173,59],{"className":174},[88,89],[14,176],{"className":177,"style":178},[134],"margin-right:0.2778em;",[14,180,62],{"className":181},[182],"mrel",[14,184],{"className":185,"style":178},[134],[14,187,189,193],{"className":188},[79],[14,190],{"className":191,"style":192},[83],"height:0.6444em;",[14,194,65],{"className":195},[88],", де ",[14,198,200,220],{"className":199},[17],[14,201,203],{"className":202},[21],[23,204,205],{"xmlns":25},[27,206,207,217],{},[30,208,209,211,215],{},[33,210,35],{},[47,212,214],{"mathvariant":213},"normal","≠",[43,216,65],{},[67,218,219],{"encoding":69},"a \\ne 0",[14,221,223,282],{"className":222,"ariaHidden":75},[74],[14,224,226,230,233,236,279],{"className":225},[79],[14,227],{"className":228,"style":229},[83],"height:0.8889em;vertical-align:-0.1944em;",[14,231,35],{"className":232},[88,89],[14,234],{"className":235,"style":178},[134],[14,237,239,272,276],{"className":238},[182],[14,240,242],{"className":241},[182],[14,243,246],{"className":244},[88,245],"vbox",[14,247,250],{"className":248},[249],"thinbox",[14,251,254,257,268],{"className":252},[253],"rlap",[14,255],{"className":256,"style":229},[83],[14,258,261],{"className":259},[260],"inner",[14,262,264],{"className":263},[88],[14,265,267],{"className":266},[182],"",[14,269],{"className":270},[271],"fix",[14,273],{"className":274},[134,275],"nobreak",[14,277,62],{"className":278},[182],[14,280],{"className":281,"style":178},[134],[14,283,285,288],{"className":284},[79],[14,286],{"className":287,"style":192},[83],[14,289,65],{"className":290},[88],". Найнадійніший спосіб його розв’язати — через ",[293,294,295],"strong",{},"дискримінант",":",[14,298,301],{"className":299},[300],"katex-display",[14,302,304,383],{"className":303},[17],[14,305,307],{"className":306},[21],[23,308,310],{"xmlns":25,"display":309},"block",[27,311,312,380],{},[30,313,314,317,319,325,328,331,333,335,338,341,355,357],{},[33,315,316],{},"D",[47,318,62],{},[37,320,321,323],{},[33,322,52],{},[43,324,45],{},[47,326,327],{},"−",[43,329,330],{},"4",[33,332,35],{},[33,334,59],{},[47,336,337],{"separator":75},",",[134,339],{"width":340},"2em",[342,343,344,346],"msub",{},[33,345,41],{},[30,347,348,351,353],{},[43,349,350],{},"1",[47,352,337],{"separator":75},[43,354,45],{},[47,356,62],{},[358,359,360,374],"mfrac",{},[30,361,362,364,366,369],{},[47,363,327],{},[33,365,52],{},[47,367,368],{},"±",[370,371,372],"msqrt",{},[33,373,316],{},[30,375,376,378],{},[43,377,45],{},[33,379,35],{},[67,381,382],{"encoding":69},"D = b^2 - 4ac, \\qquad x_{1,2} = \\frac{-b \\pm \\sqrt{D}}{2a}",[14,384,386,406,453,545],{"className":385,"ariaHidden":75},[74],[14,387,389,393,397,400,403],{"className":388},[79],[14,390],{"className":391,"style":392},[83],"height:0.6833em;",[14,394,316],{"className":395,"style":396},[88,89],"margin-right:0.0278em;",[14,398],{"className":399,"style":178},[134],[14,401,62],{"className":402},[182],[14,404],{"className":405,"style":178},[134],[14,407,409,413,444,447,450],{"className":408},[79],[14,410],{"className":411,"style":412},[83],"height:0.9474em;vertical-align:-0.0833em;",[14,414,416,419],{"className":415},[88],[14,417,52],{"className":418},[88,89],[14,420,422],{"className":421},[99],[14,423,425],{"className":424},[103],[14,426,428],{"className":427},[107],[14,429,432],{"className":430,"style":431},[111],"height:0.8641em;",[14,433,435,438],{"style":434},"top:-3.113em;margin-right:0.05em;",[14,436],{"className":437,"style":120},[119],[14,439,441],{"className":440},[124,125,126,127],[14,442,45],{"className":443},[88,127],[14,445],{"className":446,"style":135},[134],[14,448,327],{"className":449},[139],[14,451],{"className":452,"style":135},[134],[14,454,456,460,463,466,469,473,477,481,536,539,542],{"className":455},[79],[14,457],{"className":458,"style":459},[83],"height:0.9305em;vertical-align:-0.2861em;",[14,461,330],{"className":462},[88],[14,464,35],{"className":465},[88,89],[14,467,59],{"className":468},[88,89],[14,470,337],{"className":471},[472],"mpunct",[14,474],{"className":475,"style":476},[134],"margin-right:2em;",[14,478],{"className":479,"style":480},[134],"margin-right:0.1667em;",[14,482,484,487],{"className":483},[88],[14,485,41],{"className":486},[88,89],[14,488,490],{"className":489},[99],[14,491,494,527],{"className":492},[103,493],"vlist-t2",[14,495,497,522],{"className":496},[107],[14,498,501],{"className":499,"style":500},[111],"height:0.3011em;",[14,502,504,507],{"style":503},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[14,505],{"className":506,"style":120},[119],[14,508,510],{"className":509},[124,125,126,127],[14,511,513,516,519],{"className":512},[88,127],[14,514,350],{"className":515},[88,127],[14,517,337],{"className":518},[472,127],[14,520,45],{"className":521},[88,127],[14,523,526],{"className":524},[525],"vlist-s","​",[14,528,530],{"className":529},[107],[14,531,534],{"className":532,"style":533},[111],"height:0.2861em;",[14,535],{},[14,537],{"className":538,"style":178},[134],[14,540,62],{"className":541},[182],[14,543],{"className":544,"style":178},[134],[14,546,548,552],{"className":547},[79],[14,549],{"className":550,"style":551},[83],"height:2.2897em;vertical-align:-0.686em;",[14,553,555,560,700],{"className":554},[88],[14,556],{"className":557},[558,559],"mopen","nulldelimiter",[14,561,563],{"className":562},[358],[14,564,566,691],{"className":565},[103,493],[14,567,569,688],{"className":568},[107],[14,570,573,589,600],{"className":571,"style":572},[111],"height:1.6037em;",[14,574,576,580],{"style":575},"top:-2.314em;",[14,577],{"className":578,"style":579},[119],"height:3em;",[14,581,583,586],{"className":582},[88],[14,584,45],{"className":585},[88],[14,587,35],{"className":588},[88,89],[14,590,592,595],{"style":591},"top:-3.23em;",[14,593],{"className":594,"style":579},[119],[14,596],{"className":597,"style":599},[598],"frac-line","border-bottom-width:0.04em;",[14,601,603,606],{"style":602},"top:-3.677em;",[14,604],{"className":605,"style":579},[119],[14,607,609,612,615,618,621,624],{"className":608},[88],[14,610,327],{"className":611},[88],[14,613,52],{"className":614},[88,89],[14,616],{"className":617,"style":135},[134],[14,619,368],{"className":620},[139],[14,622],{"className":623,"style":135},[134],[14,625,628],{"className":626},[88,627],"sqrt",[14,629,631,679],{"className":630},[103,493],[14,632,634,676],{"className":633},[107],[14,635,638,653],{"className":636,"style":637},[111],"height:0.9267em;",[14,639,643,646],{"className":640,"style":642},[641],"svg-align","top:-3em;",[14,644],{"className":645,"style":579},[119],[14,647,650],{"className":648,"style":649},[88],"padding-left:0.833em;",[14,651,316],{"className":652,"style":396},[88,89],[14,654,656,659],{"style":655},"top:-2.8867em;",[14,657],{"className":658,"style":579},[119],[14,660,664],{"className":661,"style":663},[662],"hide-tail","min-width:0.853em;height:1.08em;",[665,666,672],"svg",{"xmlns":667,"width":668,"height":669,"viewBox":670,"preserveAspectRatio":671},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[673,674],"path",{"d":675},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[14,677,526],{"className":678},[525],[14,680,682],{"className":681},[107],[14,683,686],{"className":684,"style":685},[111],"height:0.1133em;",[14,687],{},[14,689,526],{"className":690},[525],[14,692,694],{"className":693},[107],[14,695,698],{"className":696,"style":697},[111],"height:0.686em;",[14,699],{},[14,701],{"className":702},[703,559],"mclose",[10,705,706],{},"Знак дискримінанта одразу підказує, скільки буде коренів:",[708,709,710,767,821],"ul",{},[711,712,713,766],"li",{},[14,714,716,735],{"className":715},[17],[14,717,719],{"className":718},[21],[23,720,721],{"xmlns":25},[27,722,723,732],{},[30,724,725,727,730],{},[33,726,316],{},[47,728,729],{},">",[43,731,65],{},[67,733,734],{"encoding":69},"D > 0",[14,736,738,757],{"className":737,"ariaHidden":75},[74],[14,739,741,745,748,751,754],{"className":740},[79],[14,742],{"className":743,"style":744},[83],"height:0.7224em;vertical-align:-0.0391em;",[14,746,316],{"className":747,"style":396},[88,89],[14,749],{"className":750,"style":178},[134],[14,752,729],{"className":753},[182],[14,755],{"className":756,"style":178},[134],[14,758,760,763],{"className":759},[79],[14,761],{"className":762,"style":192},[83],[14,764,65],{"className":765},[88]," — два різні корені;",[711,768,769,820],{},[14,770,772,790],{"className":771},[17],[14,773,775],{"className":774},[21],[23,776,777],{"xmlns":25},[27,778,779,787],{},[30,780,781,783,785],{},[33,782,316],{},[47,784,62],{},[43,786,65],{},[67,788,789],{"encoding":69},"D = 0",[14,791,793,811],{"className":792,"ariaHidden":75},[74],[14,794,796,799,802,805,808],{"className":795},[79],[14,797],{"className":798,"style":392},[83],[14,800,316],{"className":801,"style":396},[88,89],[14,803],{"className":804,"style":178},[134],[14,806,62],{"className":807},[182],[14,809],{"className":810,"style":178},[134],[14,812,814,817],{"className":813},[79],[14,815],{"className":816,"style":192},[83],[14,818,65],{"className":819},[88]," — один корінь;",[711,822,823,875],{},[14,824,826,845],{"className":825},[17],[14,827,829],{"className":828},[21],[23,830,831],{"xmlns":25},[27,832,833,842],{},[30,834,835,837,840],{},[33,836,316],{},[47,838,839],{},"\u003C",[43,841,65],{},[67,843,844],{"encoding":69},"D \u003C 0",[14,846,848,866],{"className":847,"ariaHidden":75},[74],[14,849,851,854,857,860,863],{"className":850},[79],[14,852],{"className":853,"style":744},[83],[14,855,316],{"className":856,"style":396},[88,89],[14,858],{"className":859,"style":178},[134],[14,861,839],{"className":862},[182],[14,864],{"className":865,"style":178},[134],[14,867,869,872],{"className":868},[79],[14,870],{"className":871,"style":192},[83],[14,873,65],{"className":874},[88]," — дійсних коренів немає.",[10,877,878,879,907,908,296],{},"Покрутіть коефіцієнти й подивіться, як знак ",[14,880,882,895],{"className":881},[17],[14,883,885],{"className":884},[21],[23,886,887],{"xmlns":25},[27,888,889,893],{},[30,890,891],{},[33,892,316],{},[67,894,316],{"encoding":69},[14,896,898],{"className":897,"ariaHidden":75},[74],[14,899,901,904],{"className":900},[79],[14,902],{"className":903,"style":392},[83],[14,905,316],{"className":906,"style":396},[88,89]," змінює кількість точок перетину з віссю ",[14,909,911,924],{"className":910},[17],[14,912,914],{"className":913},[21],[23,915,916],{"xmlns":25},[27,917,918,922],{},[30,919,920],{},[33,921,41],{},[67,923,41],{"encoding":69},[14,925,927],{"className":926,"ariaHidden":75},[74],[14,928,930,933],{"className":929},[79],[14,931],{"className":932,"style":171},[83],[14,934,41],{"className":935},[88,89],[937,938],"lab-quadratic",{},[940,941,943],"h2",{"id":942},"приклад-1-два-корені","Приклад 1. Два корені",[10,945,946,947,1080,1081,1132,1133,1132,1190,1241],{},"Розв’яжемо ",[14,948,950,984],{"className":949},[17],[14,951,953],{"className":952},[21],[23,954,955],{"xmlns":25},[27,956,957,981],{},[30,958,959,965,967,970,972,974,977,979],{},[37,960,961,963],{},[33,962,41],{},[43,964,45],{},[47,966,327],{},[43,968,969],{},"5",[33,971,41],{},[47,973,49],{},[43,975,976],{},"6",[47,978,62],{},[43,980,65],{},[67,982,983],{"encoding":69},"x^2 - 5x + 6 = 0",[14,985,987,1031,1053,1071],{"className":986,"ariaHidden":75},[74],[14,988,990,993,1022,1025,1028],{"className":989},[79],[14,991],{"className":992,"style":84},[83],[14,994,996,999],{"className":995},[88],[14,997,41],{"className":998},[88,89],[14,1000,1002],{"className":1001},[99],[14,1003,1005],{"className":1004},[103],[14,1006,1008],{"className":1007},[107],[14,1009,1011],{"className":1010,"style":112},[111],[14,1012,1013,1016],{"style":115},[14,1014],{"className":1015,"style":120},[119],[14,1017,1019],{"className":1018},[124,125,126,127],[14,1020,45],{"className":1021},[88,127],[14,1023],{"className":1024,"style":135},[134],[14,1026,327],{"className":1027},[139],[14,1029],{"className":1030,"style":135},[134],[14,1032,1034,1038,1041,1044,1047,1050],{"className":1033},[79],[14,1035],{"className":1036,"style":1037},[83],"height:0.7278em;vertical-align:-0.0833em;",[14,1039,969],{"className":1040},[88],[14,1042,41],{"className":1043},[88,89],[14,1045],{"className":1046,"style":135},[134],[14,1048,49],{"className":1049},[139],[14,1051],{"className":1052,"style":135},[134],[14,1054,1056,1059,1062,1065,1068],{"className":1055},[79],[14,1057],{"className":1058,"style":192},[83],[14,1060,976],{"className":1061},[88],[14,1063],{"className":1064,"style":178},[134],[14,1066,62],{"className":1067},[182],[14,1069],{"className":1070,"style":178},[134],[14,1072,1074,1077],{"className":1073},[79],[14,1075],{"className":1076,"style":192},[83],[14,1078,65],{"className":1079},[88],". Тут ",[14,1082,1084,1102],{"className":1083},[17],[14,1085,1087],{"className":1086},[21],[23,1088,1089],{"xmlns":25},[27,1090,1091,1099],{},[30,1092,1093,1095,1097],{},[33,1094,35],{},[47,1096,62],{},[43,1098,350],{},[67,1100,1101],{"encoding":69},"a = 1",[14,1103,1105,1123],{"className":1104,"ariaHidden":75},[74],[14,1106,1108,1111,1114,1117,1120],{"className":1107},[79],[14,1109],{"className":1110,"style":171},[83],[14,1112,35],{"className":1113},[88,89],[14,1115],{"className":1116,"style":178},[134],[14,1118,62],{"className":1119},[182],[14,1121],{"className":1122,"style":178},[134],[14,1124,1126,1129],{"className":1125},[79],[14,1127],{"className":1128,"style":192},[83],[14,1130,350],{"className":1131},[88],", ",[14,1134,1136,1156],{"className":1135},[17],[14,1137,1139],{"className":1138},[21],[23,1140,1141],{"xmlns":25},[27,1142,1143,1153],{},[30,1144,1145,1147,1149,1151],{},[33,1146,52],{},[47,1148,62],{},[47,1150,327],{},[43,1152,969],{},[67,1154,1155],{"encoding":69},"b = -5",[14,1157,1159,1178],{"className":1158,"ariaHidden":75},[74],[14,1160,1162,1166,1169,1172,1175],{"className":1161},[79],[14,1163],{"className":1164,"style":1165},[83],"height:0.6944em;",[14,1167,52],{"className":1168},[88,89],[14,1170],{"className":1171,"style":178},[134],[14,1173,62],{"className":1174},[182],[14,1176],{"className":1177,"style":178},[134],[14,1179,1181,1184,1187],{"className":1180},[79],[14,1182],{"className":1183,"style":1037},[83],[14,1185,327],{"className":1186},[88],[14,1188,969],{"className":1189},[88],[14,1191,1193,1211],{"className":1192},[17],[14,1194,1196],{"className":1195},[21],[23,1197,1198],{"xmlns":25},[27,1199,1200,1208],{},[30,1201,1202,1204,1206],{},[33,1203,59],{},[47,1205,62],{},[43,1207,976],{},[67,1209,1210],{"encoding":69},"c = 6",[14,1212,1214,1232],{"className":1213,"ariaHidden":75},[74],[14,1215,1217,1220,1223,1226,1229],{"className":1216},[79],[14,1218],{"className":1219,"style":171},[83],[14,1221,59],{"className":1222},[88,89],[14,1224],{"className":1225,"style":178},[134],[14,1227,62],{"className":1228},[182],[14,1230],{"className":1231,"style":178},[134],[14,1233,1235,1238],{"className":1234},[79],[14,1236],{"className":1237,"style":192},[83],[14,1239,976],{"className":1240},[88],".",[14,1243,1245],{"className":1244},[300],[14,1246,1248,1306],{"className":1247},[17],[14,1249,1251],{"className":1250},[21],[23,1252,1253],{"xmlns":25,"display":309},[27,1254,1255,1303],{},[30,1256,1257,1259,1261,1265,1267,1269,1276,1278,1280,1283,1285,1287,1289,1291,1294,1296,1299,1301],{},[33,1258,316],{},[47,1260,62],{},[47,1262,1264],{"stretchy":1263},"false","(",[47,1266,327],{},[43,1268,969],{},[37,1270,1271,1274],{},[47,1272,1273],{"stretchy":1263},")",[43,1275,45],{},[47,1277,327],{},[43,1279,330],{},[47,1281,1282],{},"⋅",[43,1284,350],{},[47,1286,1282],{},[43,1288,976],{},[47,1290,62],{},[43,1292,1293],{},"25",[47,1295,327],{},[43,1297,1298],{},"24",[47,1300,62],{},[43,1302,350],{},[67,1304,1305],{"encoding":69},"D = (-5)^2 - 4 \\cdot 1 \\cdot 6 = 25 - 24 = 1",[14,1307,1309,1327,1381,1399,1417,1435,1453,1471],{"className":1308,"ariaHidden":75},[74],[14,1310,1312,1315,1318,1321,1324],{"className":1311},[79],[14,1313],{"className":1314,"style":392},[83],[14,1316,316],{"className":1317,"style":396},[88,89],[14,1319],{"className":1320,"style":178},[134],[14,1322,62],{"className":1323},[182],[14,1325],{"className":1326,"style":178},[134],[14,1328,1330,1334,1337,1340,1343,1372,1375,1378],{"className":1329},[79],[14,1331],{"className":1332,"style":1333},[83],"height:1.1141em;vertical-align:-0.25em;",[14,1335,1264],{"className":1336},[558],[14,1338,327],{"className":1339},[88],[14,1341,969],{"className":1342},[88],[14,1344,1346,1349],{"className":1345},[703],[14,1347,1273],{"className":1348},[703],[14,1350,1352],{"className":1351},[99],[14,1353,1355],{"className":1354},[103],[14,1356,1358],{"className":1357},[107],[14,1359,1361],{"className":1360,"style":431},[111],[14,1362,1363,1366],{"style":434},[14,1364],{"className":1365,"style":120},[119],[14,1367,1369],{"className":1368},[124,125,126,127],[14,1370,45],{"className":1371},[88,127],[14,1373],{"className":1374,"style":135},[134],[14,1376,327],{"className":1377},[139],[14,1379],{"className":1380,"style":135},[134],[14,1382,1384,1387,1390,1393,1396],{"className":1383},[79],[14,1385],{"className":1386,"style":192},[83],[14,1388,330],{"className":1389},[88],[14,1391],{"className":1392,"style":135},[134],[14,1394,1282],{"className":1395},[139],[14,1397],{"className":1398,"style":135},[134],[14,1400,1402,1405,1408,1411,1414],{"className":1401},[79],[14,1403],{"className":1404,"style":192},[83],[14,1406,350],{"className":1407},[88],[14,1409],{"className":1410,"style":135},[134],[14,1412,1282],{"className":1413},[139],[14,1415],{"className":1416,"style":135},[134],[14,1418,1420,1423,1426,1429,1432],{"className":1419},[79],[14,1421],{"className":1422,"style":192},[83],[14,1424,976],{"className":1425},[88],[14,1427],{"className":1428,"style":178},[134],[14,1430,62],{"className":1431},[182],[14,1433],{"className":1434,"style":178},[134],[14,1436,1438,1441,1444,1447,1450],{"className":1437},[79],[14,1439],{"className":1440,"style":1037},[83],[14,1442,1293],{"className":1443},[88],[14,1445],{"className":1446,"style":135},[134],[14,1448,327],{"className":1449},[139],[14,1451],{"className":1452,"style":135},[134],[14,1454,1456,1459,1462,1465,1468],{"className":1455},[79],[14,1457],{"className":1458,"style":192},[83],[14,1460,1298],{"className":1461},[88],[14,1463],{"className":1464,"style":178},[134],[14,1466,62],{"className":1467},[182],[14,1469],{"className":1470,"style":178},[134],[14,1472,1474,1477],{"className":1473},[79],[14,1475],{"className":1476,"style":192},[83],[14,1478,350],{"className":1479},[88],[14,1481,1483],{"className":1482},[300],[14,1484,1486,1559],{"className":1485},[17],[14,1487,1489],{"className":1488},[21],[23,1490,1491],{"xmlns":25,"display":309},[27,1492,1493,1556],{},[30,1494,1495,1507,1509,1521,1524,1527,1529,1535,1537,1540,1542,1546,1552,1554],{},[342,1496,1497,1499],{},[33,1498,41],{},[30,1500,1501,1503,1505],{},[43,1502,350],{},[47,1504,337],{"separator":75},[43,1506,45],{},[47,1508,62],{},[358,1510,1511,1519],{},[30,1512,1513,1515,1517],{},[43,1514,969],{},[47,1516,368],{},[43,1518,350],{},[43,1520,45],{},[134,1522],{"width":1523},"1em",[47,1525,1526],{},"⇒",[134,1528],{"width":1523},[342,1530,1531,1533],{},[33,1532,41],{},[43,1534,350],{},[47,1536,62],{},[43,1538,1539],{},"3",[47,1541,337],{"separator":75},[1543,1544,1545],"mtext",{},"  ",[342,1547,1548,1550],{},[33,1549,41],{},[43,1551,45],{},[47,1553,62],{},[43,1555,45],{},[67,1557,1558],{"encoding":69},"x_{1,2} = \\frac{5 \\pm 1}{2} \\quad\\Rightarrow\\quad x_1 = 3,\\; x_2 = 2",[14,1560,1562,1627,1725,1782,1850],{"className":1561,"ariaHidden":75},[74],[14,1563,1565,1569,1618,1621,1624],{"className":1564},[79],[14,1566],{"className":1567,"style":1568},[83],"height:0.7167em;vertical-align:-0.2861em;",[14,1570,1572,1575],{"className":1571},[88],[14,1573,41],{"className":1574},[88,89],[14,1576,1578],{"className":1577},[99],[14,1579,1581,1610],{"className":1580},[103,493],[14,1582,1584,1607],{"className":1583},[107],[14,1585,1587],{"className":1586,"style":500},[111],[14,1588,1589,1592],{"style":503},[14,1590],{"className":1591,"style":120},[119],[14,1593,1595],{"className":1594},[124,125,126,127],[14,1596,1598,1601,1604],{"className":1597},[88,127],[14,1599,350],{"className":1600},[88,127],[14,1602,337],{"className":1603},[472,127],[14,1605,45],{"className":1606},[88,127],[14,1608,526],{"className":1609},[525],[14,1611,1613],{"className":1612},[107],[14,1614,1616],{"className":1615,"style":533},[111],[14,1617],{},[14,1619],{"className":1620,"style":178},[134],[14,1622,62],{"className":1623},[182],[14,1625],{"className":1626,"style":178},[134],[14,1628,1630,1634,1709,1713,1716,1719,1722],{"className":1629},[79],[14,1631],{"className":1632,"style":1633},[83],"height:2.0074em;vertical-align:-0.686em;",[14,1635,1637,1640,1706],{"className":1636},[88],[14,1638],{"className":1639},[558,559],[14,1641,1643],{"className":1642},[358],[14,1644,1646,1698],{"className":1645},[103,493],[14,1647,1649,1695],{"className":1648},[107],[14,1650,1653,1664,1672],{"className":1651,"style":1652},[111],"height:1.3214em;",[14,1654,1655,1658],{"style":575},[14,1656],{"className":1657,"style":579},[119],[14,1659,1661],{"className":1660},[88],[14,1662,45],{"className":1663},[88],[14,1665,1666,1669],{"style":591},[14,1667],{"className":1668,"style":579},[119],[14,1670],{"className":1671,"style":599},[598],[14,1673,1674,1677],{"style":602},[14,1675],{"className":1676,"style":579},[119],[14,1678,1680,1683,1686,1689,1692],{"className":1679},[88],[14,1681,969],{"className":1682},[88],[14,1684],{"className":1685,"style":135},[134],[14,1687,368],{"className":1688},[139],[14,1690],{"className":1691,"style":135},[134],[14,1693,350],{"className":1694},[88],[14,1696,526],{"className":1697},[525],[14,1699,1701],{"className":1700},[107],[14,1702,1704],{"className":1703,"style":697},[111],[14,1705],{},[14,1707],{"className":1708},[703,559],[14,1710],{"className":1711,"style":1712},[134],"margin-right:1em;",[14,1714],{"className":1715,"style":178},[134],[14,1717,1526],{"className":1718},[182],[14,1720],{"className":1721,"style":1712},[134],[14,1723],{"className":1724,"style":178},[134],[14,1726,1728,1732,1773,1776,1779],{"className":1727},[79],[14,1729],{"className":1730,"style":1731},[83],"height:0.5806em;vertical-align:-0.15em;",[14,1733,1735,1738],{"className":1734},[88],[14,1736,41],{"className":1737},[88,89],[14,1739,1741],{"className":1740},[99],[14,1742,1744,1764],{"className":1743},[103,493],[14,1745,1747,1761],{"className":1746},[107],[14,1748,1750],{"className":1749,"style":500},[111],[14,1751,1752,1755],{"style":503},[14,1753],{"className":1754,"style":120},[119],[14,1756,1758],{"className":1757},[124,125,126,127],[14,1759,350],{"className":1760},[88,127],[14,1762,526],{"className":1763},[525],[14,1765,1767],{"className":1766},[107],[14,1768,1771],{"className":1769,"style":1770},[111],"height:0.15em;",[14,1772],{},[14,1774],{"className":1775,"style":178},[134],[14,1777,62],{"className":1778},[182],[14,1780],{"className":1781,"style":178},[134],[14,1783,1785,1789,1792,1795,1798,1801,1841,1844,1847],{"className":1784},[79],[14,1786],{"className":1787,"style":1788},[83],"height:0.8389em;vertical-align:-0.1944em;",[14,1790,1539],{"className":1791},[88],[14,1793,337],{"className":1794},[472],[14,1796],{"className":1797,"style":178},[134],[14,1799],{"className":1800,"style":480},[134],[14,1802,1804,1807],{"className":1803},[88],[14,1805,41],{"className":1806},[88,89],[14,1808,1810],{"className":1809},[99],[14,1811,1813,1833],{"className":1812},[103,493],[14,1814,1816,1830],{"className":1815},[107],[14,1817,1819],{"className":1818,"style":500},[111],[14,1820,1821,1824],{"style":503},[14,1822],{"className":1823,"style":120},[119],[14,1825,1827],{"className":1826},[124,125,126,127],[14,1828,45],{"className":1829},[88,127],[14,1831,526],{"className":1832},[525],[14,1834,1836],{"className":1835},[107],[14,1837,1839],{"className":1838,"style":1770},[111],[14,1840],{},[14,1842],{"className":1843,"style":178},[134],[14,1845,62],{"className":1846},[182],[14,1848],{"className":1849,"style":178},[134],[14,1851,1853,1856],{"className":1852},[79],[14,1854],{"className":1855,"style":192},[83],[14,1857,45],{"className":1858},[88],[10,1860,1861,1864,1865,2125,2126,2377],{},[293,1862,1863],{},"Перевірка за теоремою Вієта:"," ",[14,1866,1868,1911],{"className":1867},[17],[14,1869,1871],{"className":1870},[21],[23,1872,1873],{"xmlns":25},[27,1874,1875,1908],{},[30,1876,1877,1883,1885,1891,1893,1895,1897,1899],{},[342,1878,1879,1881],{},[33,1880,41],{},[43,1882,350],{},[47,1884,49],{},[342,1886,1887,1889],{},[33,1888,41],{},[43,1890,45],{},[47,1892,62],{},[43,1894,969],{},[47,1896,62],{},[47,1898,327],{},[1900,1901,1902],"mstyle",{"scriptlevel":65,"displaystyle":1263},[358,1903,1904,1906],{},[33,1905,52],{},[33,1907,35],{},[67,1909,1910],{"encoding":69},"x_1 + x_2 = 5 = -\\tfrac{b}{a}",[14,1912,1914,1970,2025,2043],{"className":1913,"ariaHidden":75},[74],[14,1915,1917,1921,1961,1964,1967],{"className":1916},[79],[14,1918],{"className":1919,"style":1920},[83],"height:0.7333em;vertical-align:-0.15em;",[14,1922,1924,1927],{"className":1923},[88],[14,1925,41],{"className":1926},[88,89],[14,1928,1930],{"className":1929},[99],[14,1931,1933,1953],{"className":1932},[103,493],[14,1934,1936,1950],{"className":1935},[107],[14,1937,1939],{"className":1938,"style":500},[111],[14,1940,1941,1944],{"style":503},[14,1942],{"className":1943,"style":120},[119],[14,1945,1947],{"className":1946},[124,125,126,127],[14,1948,350],{"className":1949},[88,127],[14,1951,526],{"className":1952},[525],[14,1954,1956],{"className":1955},[107],[14,1957,1959],{"className":1958,"style":1770},[111],[14,1960],{},[14,1962],{"className":1963,"style":135},[134],[14,1965,49],{"className":1966},[139],[14,1968],{"className":1969,"style":135},[134],[14,1971,1973,1976,2016,2019,2022],{"className":1972},[79],[14,1974],{"className":1975,"style":1731},[83],[14,1977,1979,1982],{"className":1978},[88],[14,1980,41],{"className":1981},[88,89],[14,1983,1985],{"className":1984},[99],[14,1986,1988,2008],{"className":1987},[103,493],[14,1989,1991,2005],{"className":1990},[107],[14,1992,1994],{"className":1993,"style":500},[111],[14,1995,1996,1999],{"style":503},[14,1997],{"className":1998,"style":120},[119],[14,2000,2002],{"className":2001},[124,125,126,127],[14,2003,45],{"className":2004},[88,127],[14,2006,526],{"className":2007},[525],[14,2009,2011],{"className":2010},[107],[14,2012,2014],{"className":2013,"style":1770},[111],[14,2015],{},[14,2017],{"className":2018,"style":178},[134],[14,2020,62],{"className":2021},[182],[14,2023],{"className":2024,"style":178},[134],[14,2026,2028,2031,2034,2037,2040],{"className":2027},[79],[14,2029],{"className":2030,"style":192},[83],[14,2032,969],{"className":2033},[88],[14,2035],{"className":2036,"style":178},[134],[14,2038,62],{"className":2039},[182],[14,2041],{"className":2042,"style":178},[134],[14,2044,2046,2050,2053],{"className":2045},[79],[14,2047],{"className":2048,"style":2049},[83],"height:1.2251em;vertical-align:-0.345em;",[14,2051,327],{"className":2052},[88],[14,2054,2056,2059,2122],{"className":2055},[88],[14,2057],{"className":2058},[558,559],[14,2060,2062],{"className":2061},[358],[14,2063,2065,2113],{"className":2064},[103,493],[14,2066,2068,2110],{"className":2067},[107],[14,2069,2072,2087,2095],{"className":2070,"style":2071},[111],"height:0.8801em;",[14,2073,2075,2078],{"style":2074},"top:-2.655em;",[14,2076],{"className":2077,"style":579},[119],[14,2079,2081],{"className":2080},[124,125,126,127],[14,2082,2084],{"className":2083},[88,127],[14,2085,35],{"className":2086},[88,89,127],[14,2088,2089,2092],{"style":591},[14,2090],{"className":2091,"style":579},[119],[14,2093],{"className":2094,"style":599},[598],[14,2096,2098,2101],{"style":2097},"top:-3.394em;",[14,2099],{"className":2100,"style":579},[119],[14,2102,2104],{"className":2103},[124,125,126,127],[14,2105,2107],{"className":2106},[88,127],[14,2108,52],{"className":2109},[88,89,127],[14,2111,526],{"className":2112},[525],[14,2114,2116],{"className":2115},[107],[14,2117,2120],{"className":2118,"style":2119},[111],"height:0.345em;",[14,2121],{},[14,2123],{"className":2124},[703,559]," і ",[14,2127,2129,2169],{"className":2128},[17],[14,2130,2132],{"className":2131},[21],[23,2133,2134],{"xmlns":25},[27,2135,2136,2166],{},[30,2137,2138,2144,2146,2152,2154,2156,2158],{},[342,2139,2140,2142],{},[33,2141,41],{},[43,2143,350],{},[47,2145,1282],{},[342,2147,2148,2150],{},[33,2149,41],{},[43,2151,45],{},[47,2153,62],{},[43,2155,976],{},[47,2157,62],{},[1900,2159,2160],{"scriptlevel":65,"displaystyle":1263},[358,2161,2162,2164],{},[33,2163,59],{},[33,2165,35],{},[67,2167,2168],{"encoding":69},"x_1 \\cdot x_2 = 6 = \\tfrac{c}{a}",[14,2170,2172,2228,2283,2301],{"className":2171,"ariaHidden":75},[74],[14,2173,2175,2179,2219,2222,2225],{"className":2174},[79],[14,2176],{"className":2177,"style":2178},[83],"height:0.5945em;vertical-align:-0.15em;",[14,2180,2182,2185],{"className":2181},[88],[14,2183,41],{"className":2184},[88,89],[14,2186,2188],{"className":2187},[99],[14,2189,2191,2211],{"className":2190},[103,493],[14,2192,2194,2208],{"className":2193},[107],[14,2195,2197],{"className":2196,"style":500},[111],[14,2198,2199,2202],{"style":503},[14,2200],{"className":2201,"style":120},[119],[14,2203,2205],{"className":2204},[124,125,126,127],[14,2206,350],{"className":2207},[88,127],[14,2209,526],{"className":2210},[525],[14,2212,2214],{"className":2213},[107],[14,2215,2217],{"className":2216,"style":1770},[111],[14,2218],{},[14,2220],{"className":2221,"style":135},[134],[14,2223,1282],{"className":2224},[139],[14,2226],{"className":2227,"style":135},[134],[14,2229,2231,2234,2274,2277,2280],{"className":2230},[79],[14,2232],{"className":2233,"style":1731},[83],[14,2235,2237,2240],{"className":2236},[88],[14,2238,41],{"className":2239},[88,89],[14,2241,2243],{"className":2242},[99],[14,2244,2246,2266],{"className":2245},[103,493],[14,2247,2249,2263],{"className":2248},[107],[14,2250,2252],{"className":2251,"style":500},[111],[14,2253,2254,2257],{"style":503},[14,2255],{"className":2256,"style":120},[119],[14,2258,2260],{"className":2259},[124,125,126,127],[14,2261,45],{"className":2262},[88,127],[14,2264,526],{"className":2265},[525],[14,2267,2269],{"className":2268},[107],[14,2270,2272],{"className":2271,"style":1770},[111],[14,2273],{},[14,2275],{"className":2276,"style":178},[134],[14,2278,62],{"className":2279},[182],[14,2281],{"className":2282,"style":178},[134],[14,2284,2286,2289,2292,2295,2298],{"className":2285},[79],[14,2287],{"className":2288,"style":192},[83],[14,2290,976],{"className":2291},[88],[14,2293],{"className":2294,"style":178},[134],[14,2296,62],{"className":2297},[182],[14,2299],{"className":2300,"style":178},[134],[14,2302,2304,2308],{"className":2303},[79],[14,2305],{"className":2306,"style":2307},[83],"height:1.0404em;vertical-align:-0.345em;",[14,2309,2311,2314,2374],{"className":2310},[88],[14,2312],{"className":2313},[558,559],[14,2315,2317],{"className":2316},[358],[14,2318,2320,2366],{"className":2319},[103,493],[14,2321,2323,2363],{"className":2322},[107],[14,2324,2327,2341,2349],{"className":2325,"style":2326},[111],"height:0.6954em;",[14,2328,2329,2332],{"style":2074},[14,2330],{"className":2331,"style":579},[119],[14,2333,2335],{"className":2334},[124,125,126,127],[14,2336,2338],{"className":2337},[88,127],[14,2339,35],{"className":2340},[88,89,127],[14,2342,2343,2346],{"style":591},[14,2344],{"className":2345,"style":579},[119],[14,2347],{"className":2348,"style":599},[598],[14,2350,2351,2354],{"style":2097},[14,2352],{"className":2353,"style":579},[119],[14,2355,2357],{"className":2356},[124,125,126,127],[14,2358,2360],{"className":2359},[88,127],[14,2361,59],{"className":2362},[88,89,127],[14,2364,526],{"className":2365},[525],[14,2367,2369],{"className":2368},[107],[14,2370,2372],{"className":2371,"style":2119},[111],[14,2373],{},[14,2375],{"className":2376},[703,559],". Усе сходиться.",[940,2379,2381],{"id":2380},"приклад-2-один-корінь","Приклад 2. Один корінь",[10,2383,2384,2519,2520,2660],{},[14,2385,2387,2421],{"className":2386},[17],[14,2388,2390],{"className":2389},[21],[23,2391,2392],{"xmlns":25},[27,2393,2394,2418],{},[30,2395,2396,2398,2404,2406,2408,2410,2412,2414,2416],{},[43,2397,45],{},[37,2399,2400,2402],{},[33,2401,41],{},[43,2403,45],{},[47,2405,49],{},[43,2407,330],{},[33,2409,41],{},[47,2411,49],{},[43,2413,45],{},[47,2415,62],{},[43,2417,65],{},[67,2419,2420],{"encoding":69},"2x^2 + 4x + 2 = 0",[14,2422,2424,2471,2492,2510],{"className":2423,"ariaHidden":75},[74],[14,2425,2427,2430,2433,2462,2465,2468],{"className":2426},[79],[14,2428],{"className":2429,"style":84},[83],[14,2431,45],{"className":2432},[88],[14,2434,2436,2439],{"className":2435},[88],[14,2437,41],{"className":2438},[88,89],[14,2440,2442],{"className":2441},[99],[14,2443,2445],{"className":2444},[103],[14,2446,2448],{"className":2447},[107],[14,2449,2451],{"className":2450,"style":112},[111],[14,2452,2453,2456],{"style":115},[14,2454],{"className":2455,"style":120},[119],[14,2457,2459],{"className":2458},[124,125,126,127],[14,2460,45],{"className":2461},[88,127],[14,2463],{"className":2464,"style":135},[134],[14,2466,49],{"className":2467},[139],[14,2469],{"className":2470,"style":135},[134],[14,2472,2474,2477,2480,2483,2486,2489],{"className":2473},[79],[14,2475],{"className":2476,"style":1037},[83],[14,2478,330],{"className":2479},[88],[14,2481,41],{"className":2482},[88,89],[14,2484],{"className":2485,"style":135},[134],[14,2487,49],{"className":2488},[139],[14,2490],{"className":2491,"style":135},[134],[14,2493,2495,2498,2501,2504,2507],{"className":2494},[79],[14,2496],{"className":2497,"style":192},[83],[14,2499,45],{"className":2500},[88],[14,2502],{"className":2503,"style":178},[134],[14,2505,62],{"className":2506},[182],[14,2508],{"className":2509,"style":178},[134],[14,2511,2513,2516],{"className":2512},[79],[14,2514],{"className":2515,"style":192},[83],[14,2517,65],{"className":2518},[88],": ",[14,2521,2523,2558],{"className":2522},[17],[14,2524,2526],{"className":2525},[21],[23,2527,2528],{"xmlns":25},[27,2529,2530,2555],{},[30,2531,2532,2534,2536,2539,2541,2543,2545,2547,2549,2551,2553],{},[33,2533,316],{},[47,2535,62],{},[43,2537,2538],{},"16",[47,2540,327],{},[43,2542,330],{},[47,2544,1282],{},[43,2546,45],{},[47,2548,1282],{},[43,2550,45],{},[47,2552,62],{},[43,2554,65],{},[67,2556,2557],{"encoding":69},"D = 16 - 4 \\cdot 2 \\cdot 2 = 0",[14,2559,2561,2579,2597,2615,2633,2651],{"className":2560,"ariaHidden":75},[74],[14,2562,2564,2567,2570,2573,2576],{"className":2563},[79],[14,2565],{"className":2566,"style":392},[83],[14,2568,316],{"className":2569,"style":396},[88,89],[14,2571],{"className":2572,"style":178},[134],[14,2574,62],{"className":2575},[182],[14,2577],{"className":2578,"style":178},[134],[14,2580,2582,2585,2588,2591,2594],{"className":2581},[79],[14,2583],{"className":2584,"style":1037},[83],[14,2586,2538],{"className":2587},[88],[14,2589],{"className":2590,"style":135},[134],[14,2592,327],{"className":2593},[139],[14,2595],{"className":2596,"style":135},[134],[14,2598,2600,2603,2606,2609,2612],{"className":2599},[79],[14,2601],{"className":2602,"style":192},[83],[14,2604,330],{"className":2605},[88],[14,2607],{"className":2608,"style":135},[134],[14,2610,1282],{"className":2611},[139],[14,2613],{"className":2614,"style":135},[134],[14,2616,2618,2621,2624,2627,2630],{"className":2617},[79],[14,2619],{"className":2620,"style":192},[83],[14,2622,45],{"className":2623},[88],[14,2625],{"className":2626,"style":135},[134],[14,2628,1282],{"className":2629},[139],[14,2631],{"className":2632,"style":135},[134],[14,2634,2636,2639,2642,2645,2648],{"className":2635},[79],[14,2637],{"className":2638,"style":192},[83],[14,2640,45],{"className":2641},[88],[14,2643],{"className":2644,"style":178},[134],[14,2646,62],{"className":2647},[182],[14,2649],{"className":2650,"style":178},[134],[14,2652,2654,2657],{"className":2653},[79],[14,2655],{"className":2656,"style":192},[83],[14,2658,65],{"className":2659},[88],", тому",[14,2662,2664],{"className":2663},[300],[14,2665,2667,2705],{"className":2666},[17],[14,2668,2670],{"className":2669},[21],[23,2671,2672],{"xmlns":25,"display":309},[27,2673,2674,2702],{},[30,2675,2676,2678,2680,2696,2698,2700],{},[33,2677,41],{},[47,2679,62],{},[358,2681,2682,2688],{},[30,2683,2684,2686],{},[47,2685,327],{},[43,2687,330],{},[30,2689,2690,2692,2694],{},[43,2691,45],{},[47,2693,1282],{},[43,2695,45],{},[47,2697,62],{},[47,2699,327],{},[43,2701,350],{},[67,2703,2704],{"encoding":69},"x = \\frac{-4}{2 \\cdot 2} = -1",[14,2706,2708,2726,2818],{"className":2707,"ariaHidden":75},[74],[14,2709,2711,2714,2717,2720,2723],{"className":2710},[79],[14,2712],{"className":2713,"style":171},[83],[14,2715,41],{"className":2716},[88,89],[14,2718],{"className":2719,"style":178},[134],[14,2721,62],{"className":2722},[182],[14,2724],{"className":2725,"style":178},[134],[14,2727,2729,2732,2809,2812,2815],{"className":2728},[79],[14,2730],{"className":2731,"style":1633},[83],[14,2733,2735,2738,2806],{"className":2734},[88],[14,2736],{"className":2737},[558,559],[14,2739,2741],{"className":2740},[358],[14,2742,2744,2798],{"className":2743},[103,493],[14,2745,2747,2795],{"className":2746},[107],[14,2748,2750,2773,2781],{"className":2749,"style":1652},[111],[14,2751,2752,2755],{"style":575},[14,2753],{"className":2754,"style":579},[119],[14,2756,2758,2761,2764,2767,2770],{"className":2757},[88],[14,2759,45],{"className":2760},[88],[14,2762],{"className":2763,"style":135},[134],[14,2765,1282],{"className":2766},[139],[14,2768],{"className":2769,"style":135},[134],[14,2771,45],{"className":2772},[88],[14,2774,2775,2778],{"style":591},[14,2776],{"className":2777,"style":579},[119],[14,2779],{"className":2780,"style":599},[598],[14,2782,2783,2786],{"style":602},[14,2784],{"className":2785,"style":579},[119],[14,2787,2789,2792],{"className":2788},[88],[14,2790,327],{"className":2791},[88],[14,2793,330],{"className":2794},[88],[14,2796,526],{"className":2797},[525],[14,2799,2801],{"className":2800},[107],[14,2802,2804],{"className":2803,"style":697},[111],[14,2805],{},[14,2807],{"className":2808},[703,559],[14,2810],{"className":2811,"style":178},[134],[14,2813,62],{"className":2814},[182],[14,2816],{"className":2817,"style":178},[134],[14,2819,2821,2824,2827],{"className":2820},[79],[14,2822],{"className":2823,"style":1037},[83],[14,2825,327],{"className":2826},[88],[14,2828,350],{"className":2829},[88],[10,2831,2832,2833,1241],{},"Порада: рівняння можна було спершу поділити на 2 і побачити повний квадрат ",[14,2834,2836,2866],{"className":2835},[17],[14,2837,2839],{"className":2838},[21],[23,2840,2841],{"xmlns":25},[27,2842,2843,2863],{},[30,2844,2845,2847,2849,2851,2853,2859,2861],{},[47,2846,1264],{"stretchy":1263},[33,2848,41],{},[47,2850,49],{},[43,2852,350],{},[37,2854,2855,2857],{},[47,2856,1273],{"stretchy":1263},[43,2858,45],{},[47,2860,62],{},[43,2862,65],{},[67,2864,2865],{"encoding":69},"(x + 1)^2 = 0",[14,2867,2869,2891,2939],{"className":2868,"ariaHidden":75},[74],[14,2870,2872,2876,2879,2882,2885,2888],{"className":2871},[79],[14,2873],{"className":2874,"style":2875},[83],"height:1em;vertical-align:-0.25em;",[14,2877,1264],{"className":2878},[558],[14,2880,41],{"className":2881},[88,89],[14,2883],{"className":2884,"style":135},[134],[14,2886,49],{"className":2887},[139],[14,2889],{"className":2890,"style":135},[134],[14,2892,2894,2898,2901,2930,2933,2936],{"className":2893},[79],[14,2895],{"className":2896,"style":2897},[83],"height:1.0641em;vertical-align:-0.25em;",[14,2899,350],{"className":2900},[88],[14,2902,2904,2907],{"className":2903},[703],[14,2905,1273],{"className":2906},[703],[14,2908,2910],{"className":2909},[99],[14,2911,2913],{"className":2912},[103],[14,2914,2916],{"className":2915},[107],[14,2917,2919],{"className":2918,"style":112},[111],[14,2920,2921,2924],{"style":115},[14,2922],{"className":2923,"style":120},[119],[14,2925,2927],{"className":2926},[124,125,126,127],[14,2928,45],{"className":2929},[88,127],[14,2931],{"className":2932,"style":178},[134],[14,2934,62],{"className":2935},[182],[14,2937],{"className":2938,"style":178},[134],[14,2940,2942,2945],{"className":2941},[79],[14,2943],{"className":2944,"style":192},[83],[14,2946,65],{"className":2947},[88],[940,2949,2951],{"id":2950},"приклад-3-немає-коренів","Приклад 3. Немає коренів",[10,2953,2954,2519,3084,3207,3208,1241],{},[14,2955,2957,2989],{"className":2956},[17],[14,2958,2960],{"className":2959},[21],[23,2961,2962],{"xmlns":25},[27,2963,2964,2986],{},[30,2965,2966,2972,2974,2976,2978,2980,2982,2984],{},[37,2967,2968,2970],{},[33,2969,41],{},[43,2971,45],{},[47,2973,49],{},[43,2975,45],{},[33,2977,41],{},[47,2979,49],{},[43,2981,969],{},[47,2983,62],{},[43,2985,65],{},[67,2987,2988],{"encoding":69},"x^2 + 2x + 5 = 0",[14,2990,2992,3036,3057,3075],{"className":2991,"ariaHidden":75},[74],[14,2993,2995,2998,3027,3030,3033],{"className":2994},[79],[14,2996],{"className":2997,"style":84},[83],[14,2999,3001,3004],{"className":3000},[88],[14,3002,41],{"className":3003},[88,89],[14,3005,3007],{"className":3006},[99],[14,3008,3010],{"className":3009},[103],[14,3011,3013],{"className":3012},[107],[14,3014,3016],{"className":3015,"style":112},[111],[14,3017,3018,3021],{"style":115},[14,3019],{"className":3020,"style":120},[119],[14,3022,3024],{"className":3023},[124,125,126,127],[14,3025,45],{"className":3026},[88,127],[14,3028],{"className":3029,"style":135},[134],[14,3031,49],{"className":3032},[139],[14,3034],{"className":3035,"style":135},[134],[14,3037,3039,3042,3045,3048,3051,3054],{"className":3038},[79],[14,3040],{"className":3041,"style":1037},[83],[14,3043,45],{"className":3044},[88],[14,3046,41],{"className":3047},[88,89],[14,3049],{"className":3050,"style":135},[134],[14,3052,49],{"className":3053},[139],[14,3055],{"className":3056,"style":135},[134],[14,3058,3060,3063,3066,3069,3072],{"className":3059},[79],[14,3061],{"className":3062,"style":192},[83],[14,3064,969],{"className":3065},[88],[14,3067],{"className":3068,"style":178},[134],[14,3070,62],{"className":3071},[182],[14,3073],{"className":3074,"style":178},[134],[14,3076,3078,3081],{"className":3077},[79],[14,3079],{"className":3080,"style":192},[83],[14,3082,65],{"className":3083},[88],[14,3085,3087,3120],{"className":3086},[17],[14,3088,3090],{"className":3089},[21],[23,3091,3092],{"xmlns":25},[27,3093,3094,3117],{},[30,3095,3096,3098,3100,3102,3104,3107,3109,3111,3113,3115],{},[33,3097,316],{},[47,3099,62],{},[43,3101,330],{},[47,3103,327],{},[43,3105,3106],{},"20",[47,3108,62],{},[47,3110,327],{},[43,3112,2538],{},[47,3114,839],{},[43,3116,65],{},[67,3118,3119],{"encoding":69},"D = 4 - 20 = -16 \u003C 0",[14,3121,3123,3141,3159,3177,3198],{"className":3122,"ariaHidden":75},[74],[14,3124,3126,3129,3132,3135,3138],{"className":3125},[79],[14,3127],{"className":3128,"style":392},[83],[14,3130,316],{"className":3131,"style":396},[88,89],[14,3133],{"className":3134,"style":178},[134],[14,3136,62],{"className":3137},[182],[14,3139],{"className":3140,"style":178},[134],[14,3142,3144,3147,3150,3153,3156],{"className":3143},[79],[14,3145],{"className":3146,"style":1037},[83],[14,3148,330],{"className":3149},[88],[14,3151],{"className":3152,"style":135},[134],[14,3154,327],{"className":3155},[139],[14,3157],{"className":3158,"style":135},[134],[14,3160,3162,3165,3168,3171,3174],{"className":3161},[79],[14,3163],{"className":3164,"style":192},[83],[14,3166,3106],{"className":3167},[88],[14,3169],{"className":3170,"style":178},[134],[14,3172,62],{"className":3173},[182],[14,3175],{"className":3176,"style":178},[134],[14,3178,3180,3183,3186,3189,3192,3195],{"className":3179},[79],[14,3181],{"className":3182,"style":1037},[83],[14,3184,327],{"className":3185},[88],[14,3187,2538],{"className":3188},[88],[14,3190],{"className":3191,"style":178},[134],[14,3193,839],{"className":3194},[182],[14,3196],{"className":3197,"style":178},[134],[14,3199,3201,3204],{"className":3200},[79],[14,3202],{"className":3203,"style":192},[83],[14,3205,65],{"className":3206},[88],". Квадратний корінь з від’ємного числа серед дійсних чисел не існує — ",[293,3209,3210],{},"коренів немає",[940,3212,3214],{"id":3213},"приклад-4-задача-з-параметром-як-на-нмт","Приклад 4. Задача з параметром (як на НМТ)",[3216,3217,3218],"blockquote",{},[10,3219,3220,3221,3249,3250,3380],{},"При якому значенні ",[14,3222,3224,3237],{"className":3223},[17],[14,3225,3227],{"className":3226},[21],[23,3228,3229],{"xmlns":25},[27,3230,3231,3235],{},[30,3232,3233],{},[33,3234,35],{},[67,3236,35],{"encoding":69},[14,3238,3240],{"className":3239,"ariaHidden":75},[74],[14,3241,3243,3246],{"className":3242},[79],[14,3244],{"className":3245,"style":171},[83],[14,3247,35],{"className":3248},[88,89]," рівняння ",[14,3251,3253,3285],{"className":3252},[17],[14,3254,3256],{"className":3255},[21],[23,3257,3258],{"xmlns":25},[27,3259,3260,3282],{},[30,3261,3262,3268,3270,3272,3274,3276,3278,3280],{},[37,3263,3264,3266],{},[33,3265,41],{},[43,3267,45],{},[47,3269,327],{},[43,3271,330],{},[33,3273,41],{},[47,3275,49],{},[33,3277,35],{},[47,3279,62],{},[43,3281,65],{},[67,3283,3284],{"encoding":69},"x^2 - 4x + a = 0",[14,3286,3288,3332,3353,3371],{"className":3287,"ariaHidden":75},[74],[14,3289,3291,3294,3323,3326,3329],{"className":3290},[79],[14,3292],{"className":3293,"style":84},[83],[14,3295,3297,3300],{"className":3296},[88],[14,3298,41],{"className":3299},[88,89],[14,3301,3303],{"className":3302},[99],[14,3304,3306],{"className":3305},[103],[14,3307,3309],{"className":3308},[107],[14,3310,3312],{"className":3311,"style":112},[111],[14,3313,3314,3317],{"style":115},[14,3315],{"className":3316,"style":120},[119],[14,3318,3320],{"className":3319},[124,125,126,127],[14,3321,45],{"className":3322},[88,127],[14,3324],{"className":3325,"style":135},[134],[14,3327,327],{"className":3328},[139],[14,3330],{"className":3331,"style":135},[134],[14,3333,3335,3338,3341,3344,3347,3350],{"className":3334},[79],[14,3336],{"className":3337,"style":1037},[83],[14,3339,330],{"className":3340},[88],[14,3342,41],{"className":3343},[88,89],[14,3345],{"className":3346,"style":135},[134],[14,3348,49],{"className":3349},[139],[14,3351],{"className":3352,"style":135},[134],[14,3354,3356,3359,3362,3365,3368],{"className":3355},[79],[14,3357],{"className":3358,"style":171},[83],[14,3360,35],{"className":3361},[88,89],[14,3363],{"className":3364,"style":178},[134],[14,3366,62],{"className":3367},[182],[14,3369],{"className":3370,"style":178},[134],[14,3372,3374,3377],{"className":3373},[79],[14,3375],{"className":3376,"style":192},[83],[14,3378,65],{"className":3379},[88]," має рівно один корінь?",[10,3382,3383,3384,296],{},"Один корінь означає ",[14,3385,3387,3404],{"className":3386},[17],[14,3388,3390],{"className":3389},[21],[23,3391,3392],{"xmlns":25},[27,3393,3394,3402],{},[30,3395,3396,3398,3400],{},[33,3397,316],{},[47,3399,62],{},[43,3401,65],{},[67,3403,789],{"encoding":69},[14,3405,3407,3425],{"className":3406,"ariaHidden":75},[74],[14,3408,3410,3413,3416,3419,3422],{"className":3409},[79],[14,3411],{"className":3412,"style":392},[83],[14,3414,316],{"className":3415,"style":396},[88,89],[14,3417],{"className":3418,"style":178},[134],[14,3420,62],{"className":3421},[182],[14,3423],{"className":3424,"style":178},[134],[14,3426,3428,3431],{"className":3427},[79],[14,3429],{"className":3430,"style":192},[83],[14,3432,65],{"className":3433},[88],[14,3435,3437],{"className":3436},[300],[14,3438,3440,3480],{"className":3439},[17],[14,3441,3443],{"className":3442},[21],[23,3444,3445],{"xmlns":25,"display":309},[27,3446,3447,3477],{},[30,3448,3449,3451,3453,3455,3457,3459,3461,3463,3465,3467,3469,3471,3473,3475],{},[33,3450,316],{},[47,3452,62],{},[43,3454,2538],{},[47,3456,327],{},[43,3458,330],{},[33,3460,35],{},[47,3462,62],{},[43,3464,65],{},[134,3466],{"width":1523},[47,3468,1526],{},[134,3470],{"width":1523},[33,3472,35],{},[47,3474,62],{},[43,3476,330],{},[67,3478,3479],{"encoding":69},"D = 16 - 4a = 0 \\quad\\Rightarrow\\quad a = 4",[14,3481,3483,3501,3519,3540,3564,3582],{"className":3482,"ariaHidden":75},[74],[14,3484,3486,3489,3492,3495,3498],{"className":3485},[79],[14,3487],{"className":3488,"style":392},[83],[14,3490,316],{"className":3491,"style":396},[88,89],[14,3493],{"className":3494,"style":178},[134],[14,3496,62],{"className":3497},[182],[14,3499],{"className":3500,"style":178},[134],[14,3502,3504,3507,3510,3513,3516],{"className":3503},[79],[14,3505],{"className":3506,"style":1037},[83],[14,3508,2538],{"className":3509},[88],[14,3511],{"className":3512,"style":135},[134],[14,3514,327],{"className":3515},[139],[14,3517],{"className":3518,"style":135},[134],[14,3520,3522,3525,3528,3531,3534,3537],{"className":3521},[79],[14,3523],{"className":3524,"style":192},[83],[14,3526,330],{"className":3527},[88],[14,3529,35],{"className":3530},[88,89],[14,3532],{"className":3533,"style":178},[134],[14,3535,62],{"className":3536},[182],[14,3538],{"className":3539,"style":178},[134],[14,3541,3543,3546,3549,3552,3555,3558,3561],{"className":3542},[79],[14,3544],{"className":3545,"style":192},[83],[14,3547,65],{"className":3548},[88],[14,3550],{"className":3551,"style":1712},[134],[14,3553],{"className":3554,"style":178},[134],[14,3556,1526],{"className":3557},[182],[14,3559],{"className":3560,"style":1712},[134],[14,3562],{"className":3563,"style":178},[134],[14,3565,3567,3570,3573,3576,3579],{"className":3566},[79],[14,3568],{"className":3569,"style":171},[83],[14,3571,35],{"className":3572},[88,89],[14,3574],{"className":3575,"style":178},[134],[14,3577,62],{"className":3578},[182],[14,3580],{"className":3581,"style":178},[134],[14,3583,3585,3588],{"className":3584},[79],[14,3586],{"className":3587,"style":192},[83],[14,3589,330],{"className":3590},[88],[10,3592,3593,1864,3596,1241],{},[293,3594,3595],{},"Відповідь:",[14,3597,3599,3617],{"className":3598},[17],[14,3600,3602],{"className":3601},[21],[23,3603,3604],{"xmlns":25},[27,3605,3606,3614],{},[30,3607,3608,3610,3612],{},[33,3609,35],{},[47,3611,62],{},[43,3613,330],{},[67,3615,3616],{"encoding":69},"a = 4",[14,3618,3620,3638],{"className":3619,"ariaHidden":75},[74],[14,3621,3623,3626,3629,3632,3635],{"className":3622},[79],[14,3624],{"className":3625,"style":171},[83],[14,3627,35],{"className":3628},[88,89],[14,3630],{"className":3631,"style":178},[134],[14,3633,62],{"className":3634},[182],[14,3636],{"className":3637,"style":178},[134],[14,3639,3641,3644],{"className":3640},[79],[14,3642],{"className":3643,"style":192},[83],[14,3645,330],{"className":3646},[88],[940,3648,3650],{"id":3649},"типові-помилки","Типові помилки",[3652,3653,3654,3917,4094],"ol",{},[711,3655,3656,3687,3688,3743,3744,3800,3801,3882,3883,1241],{},[293,3657,3658,3659,1241],{},"Губиться знак ",[14,3660,3662,3675],{"className":3661},[17],[14,3663,3665],{"className":3664},[21],[23,3666,3667],{"xmlns":25},[27,3668,3669,3673],{},[30,3670,3671],{},[33,3672,52],{},[67,3674,52],{"encoding":69},[14,3676,3678],{"className":3677,"ariaHidden":75},[74],[14,3679,3681,3684],{"className":3680},[79],[14,3682],{"className":3683,"style":1165},[83],[14,3685,52],{"className":3686},[88,89]," Якщо ",[14,3689,3691,3710],{"className":3690},[17],[14,3692,3694],{"className":3693},[21],[23,3695,3696],{"xmlns":25},[27,3697,3698,3708],{},[30,3699,3700,3702,3704,3706],{},[33,3701,52],{},[47,3703,62],{},[47,3705,327],{},[43,3707,969],{},[67,3709,1155],{"encoding":69},[14,3711,3713,3731],{"className":3712,"ariaHidden":75},[74],[14,3714,3716,3719,3722,3725,3728],{"className":3715},[79],[14,3717],{"className":3718,"style":1165},[83],[14,3720,52],{"className":3721},[88,89],[14,3723],{"className":3724,"style":178},[134],[14,3726,62],{"className":3727},[182],[14,3729],{"className":3730,"style":178},[134],[14,3732,3734,3737,3740],{"className":3733},[79],[14,3735],{"className":3736,"style":1037},[83],[14,3738,327],{"className":3739},[88],[14,3741,969],{"className":3742},[88],", то ",[14,3745,3747,3767],{"className":3746},[17],[14,3748,3750],{"className":3749},[21],[23,3751,3752],{"xmlns":25},[27,3753,3754,3764],{},[30,3755,3756,3758,3760,3762],{},[47,3757,327],{},[33,3759,52],{},[47,3761,62],{},[43,3763,969],{},[67,3765,3766],{"encoding":69},"-b = 5",[14,3768,3770,3791],{"className":3769,"ariaHidden":75},[74],[14,3771,3773,3776,3779,3782,3785,3788],{"className":3772},[79],[14,3774],{"className":3775,"style":149},[83],[14,3777,327],{"className":3778},[88],[14,3780,52],{"className":3781},[88,89],[14,3783],{"className":3784,"style":178},[134],[14,3786,62],{"className":3787},[182],[14,3789],{"className":3790,"style":178},[134],[14,3792,3794,3797],{"className":3793},[79],[14,3795],{"className":3796,"style":192},[83],[14,3798,969],{"className":3799},[88],", а ",[14,3802,3804,3826],{"className":3803},[17],[14,3805,3807],{"className":3806},[21],[23,3808,3809],{"xmlns":25},[27,3810,3811,3823],{},[30,3812,3813,3819,3821],{},[37,3814,3815,3817],{},[33,3816,52],{},[43,3818,45],{},[47,3820,62],{},[43,3822,1293],{},[67,3824,3825],{"encoding":69},"b^2 = 25",[14,3827,3829,3873],{"className":3828,"ariaHidden":75},[74],[14,3830,3832,3835,3864,3867,3870],{"className":3831},[79],[14,3833],{"className":3834,"style":112},[83],[14,3836,3838,3841],{"className":3837},[88],[14,3839,52],{"className":3840},[88,89],[14,3842,3844],{"className":3843},[99],[14,3845,3847],{"className":3846},[103],[14,3848,3850],{"className":3849},[107],[14,3851,3853],{"className":3852,"style":112},[111],[14,3854,3855,3858],{"style":115},[14,3856],{"className":3857,"style":120},[119],[14,3859,3861],{"className":3860},[124,125,126,127],[14,3862,45],{"className":3863},[88,127],[14,3865],{"className":3866,"style":178},[134],[14,3868,62],{"className":3869},[182],[14,3871],{"className":3872,"style":178},[134],[14,3874,3876,3879],{"className":3875},[79],[14,3877],{"className":3878,"style":192},[83],[14,3880,1293],{"className":3881},[88],", а не ",[14,3884,3886,3902],{"className":3885},[17],[14,3887,3889],{"className":3888},[21],[23,3890,3891],{"xmlns":25},[27,3892,3893,3899],{},[30,3894,3895,3897],{},[47,3896,327],{},[43,3898,1293],{},[67,3900,3901],{"encoding":69},"-25",[14,3903,3905],{"className":3904,"ariaHidden":75},[74],[14,3906,3908,3911,3914],{"className":3907},[79],[14,3909],{"className":3910,"style":1037},[83],[14,3912,327],{"className":3913},[88],[14,3915,1293],{"className":3916},[88],[711,3918,3919,3956,3957,3990,3991,1241],{},[293,3920,3921,3922,1241],{},"Ділять лише корінь на ",[14,3923,3925,3941],{"className":3924},[17],[14,3926,3928],{"className":3927},[21],[23,3929,3930],{"xmlns":25},[27,3931,3932,3938],{},[30,3933,3934,3936],{},[43,3935,45],{},[33,3937,35],{},[67,3939,3940],{"encoding":69},"2a",[14,3942,3944],{"className":3943,"ariaHidden":75},[74],[14,3945,3947,3950,3953],{"className":3946},[79],[14,3948],{"className":3949,"style":192},[83],[14,3951,45],{"className":3952},[88],[14,3954,35],{"className":3955},[88,89]," На ",[14,3958,3960,3975],{"className":3959},[17],[14,3961,3963],{"className":3962},[21],[23,3964,3965],{"xmlns":25},[27,3966,3967,3973],{},[30,3968,3969,3971],{},[43,3970,45],{},[33,3972,35],{},[67,3974,3940],{"encoding":69},[14,3976,3978],{"className":3977,"ariaHidden":75},[74],[14,3979,3981,3984,3987],{"className":3980},[79],[14,3982],{"className":3983,"style":192},[83],[14,3985,45],{"className":3986},[88],[14,3988,35],{"className":3989},[88,89]," ділиться весь чисельник ",[14,3992,3994,4016],{"className":3993},[17],[14,3995,3997],{"className":3996},[21],[23,3998,3999],{"xmlns":25},[27,4000,4001,4013],{},[30,4002,4003,4005,4007,4009],{},[47,4004,327],{},[33,4006,52],{},[47,4008,368],{},[370,4010,4011],{},[33,4012,316],{},[67,4014,4015],{"encoding":69},"-b \\pm \\sqrt{D}",[14,4017,4019,4040],{"className":4018,"ariaHidden":75},[74],[14,4020,4022,4025,4028,4031,4034,4037],{"className":4021},[79],[14,4023],{"className":4024,"style":149},[83],[14,4026,327],{"className":4027},[88],[14,4029,52],{"className":4030},[88,89],[14,4032],{"className":4033,"style":135},[134],[14,4035,368],{"className":4036},[139],[14,4038],{"className":4039,"style":135},[134],[14,4041,4043,4047],{"className":4042},[79],[14,4044],{"className":4045,"style":4046},[83],"height:1.04em;vertical-align:-0.1133em;",[14,4048,4050],{"className":4049},[88,627],[14,4051,4053,4086],{"className":4052},[103,493],[14,4054,4056,4083],{"className":4055},[107],[14,4057,4059,4071],{"className":4058,"style":637},[111],[14,4060,4062,4065],{"className":4061,"style":642},[641],[14,4063],{"className":4064,"style":579},[119],[14,4066,4068],{"className":4067,"style":649},[88],[14,4069,316],{"className":4070,"style":396},[88,89],[14,4072,4073,4076],{"style":655},[14,4074],{"className":4075,"style":579},[119],[14,4077,4079],{"className":4078,"style":663},[662],[665,4080,4081],{"xmlns":667,"width":668,"height":669,"viewBox":670,"preserveAspectRatio":671},[673,4082],{"d":675},[14,4084,526],{"className":4085},[525],[14,4087,4089],{"className":4088},[107],[14,4090,4092],{"className":4091,"style":685},[111],[14,4093],{},[711,4095,4096,3687,4182,4233],{},[293,4097,4098,4099,1241],{},"Забувають про ",[14,4100,4102,4119],{"className":4101},[17],[14,4103,4105],{"className":4104},[21],[23,4106,4107],{"xmlns":25},[27,4108,4109,4117],{},[30,4110,4111,4113,4115],{},[33,4112,35],{},[47,4114,214],{"mathvariant":213},[43,4116,65],{},[67,4118,219],{"encoding":69},[14,4120,4122,4173],{"className":4121,"ariaHidden":75},[74],[14,4123,4125,4128,4131,4134,4170],{"className":4124},[79],[14,4126],{"className":4127,"style":229},[83],[14,4129,35],{"className":4130},[88,89],[14,4132],{"className":4133,"style":178},[134],[14,4135,4137,4164,4167],{"className":4136},[182],[14,4138,4140],{"className":4139},[182],[14,4141,4143],{"className":4142},[88,245],[14,4144,4146],{"className":4145},[249],[14,4147,4149,4152,4161],{"className":4148},[253],[14,4150],{"className":4151,"style":229},[83],[14,4153,4155],{"className":4154},[260],[14,4156,4158],{"className":4157},[88],[14,4159,267],{"className":4160},[182],[14,4162],{"className":4163},[271],[14,4165],{"className":4166},[134,275],[14,4168,62],{"className":4169},[182],[14,4171],{"className":4172,"style":178},[134],[14,4174,4176,4179],{"className":4175},[79],[14,4177],{"className":4178,"style":192},[83],[14,4180,65],{"className":4181},[88],[14,4183,4185,4203],{"className":4184},[17],[14,4186,4188],{"className":4187},[21],[23,4189,4190],{"xmlns":25},[27,4191,4192,4200],{},[30,4193,4194,4196,4198],{},[33,4195,35],{},[47,4197,62],{},[43,4199,65],{},[67,4201,4202],{"encoding":69},"a = 0",[14,4204,4206,4224],{"className":4205,"ariaHidden":75},[74],[14,4207,4209,4212,4215,4218,4221],{"className":4208},[79],[14,4210],{"className":4211,"style":171},[83],[14,4213,35],{"className":4214},[88,89],[14,4216],{"className":4217,"style":178},[134],[14,4219,62],{"className":4220},[182],[14,4222],{"className":4223,"style":178},[134],[14,4225,4227,4230],{"className":4226},[79],[14,4228],{"className":4229,"style":192},[83],[14,4231,65],{"className":4232},[88],", рівняння вже лінійне, і формула не працює.",[940,4235,4237],{"id":4236},"спробуйте-самі","Спробуйте самі",[10,4239,4240,4241,1241],{},"Розв’яжіть ",[14,4242,4244,4279],{"className":4243},[17],[14,4245,4247],{"className":4246},[21],[23,4248,4249],{"xmlns":25},[27,4250,4251,4276],{},[30,4252,4253,4255,4261,4263,4266,4268,4270,4272,4274],{},[43,4254,1539],{},[37,4256,4257,4259],{},[33,4258,41],{},[43,4260,45],{},[47,4262,327],{},[43,4264,4265],{},"7",[33,4267,41],{},[47,4269,49],{},[43,4271,45],{},[47,4273,62],{},[43,4275,65],{},[67,4277,4278],{"encoding":69},"3x^2 - 7x + 2 = 0",[14,4280,4282,4329,4350,4368],{"className":4281,"ariaHidden":75},[74],[14,4283,4285,4288,4291,4320,4323,4326],{"className":4284},[79],[14,4286],{"className":4287,"style":84},[83],[14,4289,1539],{"className":4290},[88],[14,4292,4294,4297],{"className":4293},[88],[14,4295,41],{"className":4296},[88,89],[14,4298,4300],{"className":4299},[99],[14,4301,4303],{"className":4302},[103],[14,4304,4306],{"className":4305},[107],[14,4307,4309],{"className":4308,"style":112},[111],[14,4310,4311,4314],{"style":115},[14,4312],{"className":4313,"style":120},[119],[14,4315,4317],{"className":4316},[124,125,126,127],[14,4318,45],{"className":4319},[88,127],[14,4321],{"className":4322,"style":135},[134],[14,4324,327],{"className":4325},[139],[14,4327],{"className":4328,"style":135},[134],[14,4330,4332,4335,4338,4341,4344,4347],{"className":4331},[79],[14,4333],{"className":4334,"style":1037},[83],[14,4336,4265],{"className":4337},[88],[14,4339,41],{"className":4340},[88,89],[14,4342],{"className":4343,"style":135},[134],[14,4345,49],{"className":4346},[139],[14,4348],{"className":4349,"style":135},[134],[14,4351,4353,4356,4359,4362,4365],{"className":4352},[79],[14,4354],{"className":4355,"style":192},[83],[14,4357,45],{"className":4358},[88],[14,4360],{"className":4361,"style":178},[134],[14,4363,62],{"className":4364},[182],[14,4366],{"className":4367,"style":178},[134],[14,4369,4371,4374],{"className":4370},[79],[14,4372],{"className":4373,"style":192},[83],[14,4375,65],{"className":4376},[88],[4378,4379,4380],"answer",{},[10,4381,4382,4383,1132,4479,1132,4571,1241],{},"Відповідь: ",[14,4384,4386,4413],{"className":4385},[17],[14,4387,4389],{"className":4388},[21],[23,4390,4391],{"xmlns":25},[27,4392,4393,4410],{},[30,4394,4395,4397,4399,4402,4404,4406,4408],{},[33,4396,316],{},[47,4398,62],{},[43,4400,4401],{},"49",[47,4403,327],{},[43,4405,1298],{},[47,4407,62],{},[43,4409,1293],{},[67,4411,4412],{"encoding":69},"D = 49 - 24 = 25",[14,4414,4416,4434,4452,4470],{"className":4415,"ariaHidden":75},[74],[14,4417,4419,4422,4425,4428,4431],{"className":4418},[79],[14,4420],{"className":4421,"style":392},[83],[14,4423,316],{"className":4424,"style":396},[88,89],[14,4426],{"className":4427,"style":178},[134],[14,4429,62],{"className":4430},[182],[14,4432],{"className":4433,"style":178},[134],[14,4435,4437,4440,4443,4446,4449],{"className":4436},[79],[14,4438],{"className":4439,"style":1037},[83],[14,4441,4401],{"className":4442},[88],[14,4444],{"className":4445,"style":135},[134],[14,4447,327],{"className":4448},[139],[14,4450],{"className":4451,"style":135},[134],[14,4453,4455,4458,4461,4464,4467],{"className":4454},[79],[14,4456],{"className":4457,"style":192},[83],[14,4459,1298],{"className":4460},[88],[14,4462],{"className":4463,"style":178},[134],[14,4465,62],{"className":4466},[182],[14,4468],{"className":4469,"style":178},[134],[14,4471,4473,4476],{"className":4472},[79],[14,4474],{"className":4475,"style":192},[83],[14,4477,1293],{"className":4478},[88],[14,4480,4482,4504],{"className":4481},[17],[14,4483,4485],{"className":4484},[21],[23,4486,4487],{"xmlns":25},[27,4488,4489,4501],{},[30,4490,4491,4497,4499],{},[342,4492,4493,4495],{},[33,4494,41],{},[43,4496,350],{},[47,4498,62],{},[43,4500,45],{},[67,4502,4503],{"encoding":69},"x_1 = 2",[14,4505,4507,4562],{"className":4506,"ariaHidden":75},[74],[14,4508,4510,4513,4553,4556,4559],{"className":4509},[79],[14,4511],{"className":4512,"style":1731},[83],[14,4514,4516,4519],{"className":4515},[88],[14,4517,41],{"className":4518},[88,89],[14,4520,4522],{"className":4521},[99],[14,4523,4525,4545],{"className":4524},[103,493],[14,4526,4528,4542],{"className":4527},[107],[14,4529,4531],{"className":4530,"style":500},[111],[14,4532,4533,4536],{"style":503},[14,4534],{"className":4535,"style":120},[119],[14,4537,4539],{"className":4538},[124,125,126,127],[14,4540,350],{"className":4541},[88,127],[14,4543,526],{"className":4544},[525],[14,4546,4548],{"className":4547},[107],[14,4549,4551],{"className":4550,"style":1770},[111],[14,4552],{},[14,4554],{"className":4555,"style":178},[134],[14,4557,62],{"className":4558},[182],[14,4560],{"className":4561,"style":178},[134],[14,4563,4565,4568],{"className":4564},[79],[14,4566],{"className":4567,"style":192},[83],[14,4569,45],{"className":4570},[88],[14,4572,4574,4602],{"className":4573},[17],[14,4575,4577],{"className":4576},[21],[23,4578,4579],{"xmlns":25},[27,4580,4581,4599],{},[30,4582,4583,4589,4591],{},[342,4584,4585,4587],{},[33,4586,41],{},[43,4588,45],{},[47,4590,62],{},[1900,4592,4593],{"scriptlevel":65,"displaystyle":1263},[358,4594,4595,4597],{},[43,4596,350],{},[43,4598,1539],{},[67,4600,4601],{"encoding":69},"x_2 = \\tfrac{1}{3}",[14,4603,4605,4660],{"className":4604,"ariaHidden":75},[74],[14,4606,4608,4611,4651,4654,4657],{"className":4607},[79],[14,4609],{"className":4610,"style":1731},[83],[14,4612,4614,4617],{"className":4613},[88],[14,4615,41],{"className":4616},[88,89],[14,4618,4620],{"className":4619},[99],[14,4621,4623,4643],{"className":4622},[103,493],[14,4624,4626,4640],{"className":4625},[107],[14,4627,4629],{"className":4628,"style":500},[111],[14,4630,4631,4634],{"style":503},[14,4632],{"className":4633,"style":120},[119],[14,4635,4637],{"className":4636},[124,125,126,127],[14,4638,45],{"className":4639},[88,127],[14,4641,526],{"className":4642},[525],[14,4644,4646],{"className":4645},[107],[14,4647,4649],{"className":4648,"style":1770},[111],[14,4650],{},[14,4652],{"className":4653,"style":178},[134],[14,4655,62],{"className":4656},[182],[14,4658],{"className":4659,"style":178},[134],[14,4661,4663,4667],{"className":4662},[79],[14,4664],{"className":4665,"style":4666},[83],"height:1.1901em;vertical-align:-0.345em;",[14,4668,4670,4673,4733],{"className":4669},[88],[14,4671],{"className":4672},[558,559],[14,4674,4676],{"className":4675},[358],[14,4677,4679,4725],{"className":4678},[103,493],[14,4680,4682,4722],{"className":4681},[107],[14,4683,4686,4700,4708],{"className":4684,"style":4685},[111],"height:0.8451em;",[14,4687,4688,4691],{"style":2074},[14,4689],{"className":4690,"style":579},[119],[14,4692,4694],{"className":4693},[124,125,126,127],[14,4695,4697],{"className":4696},[88,127],[14,4698,1539],{"className":4699},[88,127],[14,4701,4702,4705],{"style":591},[14,4703],{"className":4704,"style":579},[119],[14,4706],{"className":4707,"style":599},[598],[14,4709,4710,4713],{"style":2097},[14,4711],{"className":4712,"style":579},[119],[14,4714,4716],{"className":4715},[124,125,126,127],[14,4717,4719],{"className":4718},[88,127],[14,4720,350],{"className":4721},[88,127],[14,4723,526],{"className":4724},[525],[14,4726,4728],{"className":4727},[107],[14,4729,4731],{"className":4730,"style":2119},[111],[14,4732],{},[14,4734],{"className":4735},[703,559],{"title":4737,"searchDepth":4738,"depth":4739,"links":4740},"",2,3,[4741,4742,4743,4744,4745,4746],{"id":942,"depth":4738,"text":943},{"id":2380,"depth":4738,"text":2381},{"id":2950,"depth":4738,"text":2951},{"id":3213,"depth":4738,"text":3214},{"id":3649,"depth":4738,"text":3650},{"id":4236,"depth":4738,"text":4237},"2026-10-10","Покроково розв’язуємо квадратні рівняння через дискримінант: два корені, один корінь, немає коренів і задача з параметром у стилі НМТ.",false,"md","8",null,{},true,"\u002Fblog\u002Fkvadratni-rivnyannya-dyskryminant","---\ntitle: 'Квадратні рівняння, 8 клас: пояснення через дискримінант і приклади'\ndescription: 'Покроково розв’язуємо квадратні рівняння через дискримінант: два корені, один корінь, немає коренів і задача з параметром у стилі НМТ.'\ndate: '2026-10-10'\nsubject: math\ngrade: 8\ntopic: 'Квадратні рівняння'\ntags: [квадратні рівняння, дискримінант, НМТ, алгебра]\n---\n\nКвадратне рівняння має вигляд $ax^2 + bx + c = 0$, де $a \\ne 0$. Найнадійніший спосіб його розв’язати — через **дискримінант**:\n\n$$\nD = b^2 - 4ac, \\qquad x_{1,2} = \\frac{-b \\pm \\sqrt{D}}{2a}\n$$\n\nЗнак дискримінанта одразу підказує, скільки буде коренів:\n\n- $D > 0$ — два різні корені;\n- $D = 0$ — один корінь;\n- $D \u003C 0$ — дійсних коренів немає.\n\nПокрутіть коефіцієнти й подивіться, як знак $D$ змінює кількість точок перетину з віссю $x$:\n\n::lab-quadratic\n::\n\n## Приклад 1. Два корені\n\nРозв’яжемо $x^2 - 5x + 6 = 0$. Тут $a = 1$, $b = -5$, $c = 6$.\n\n$$\nD = (-5)^2 - 4 \\cdot 1 \\cdot 6 = 25 - 24 = 1\n$$\n\n$$\nx_{1,2} = \\frac{5 \\pm 1}{2} \\quad\\Rightarrow\\quad x_1 = 3,\\; x_2 = 2\n$$\n\n**Перевірка за теоремою Вієта:** $x_1 + x_2 = 5 = -\\tfrac{b}{a}$ і $x_1 \\cdot x_2 = 6 = \\tfrac{c}{a}$. Усе сходиться.\n\n## Приклад 2. Один корінь\n\n$2x^2 + 4x + 2 = 0$: $D = 16 - 4 \\cdot 2 \\cdot 2 = 0$, тому\n\n$$\nx = \\frac{-4}{2 \\cdot 2} = -1\n$$\n\nПорада: рівняння можна було спершу поділити на 2 і побачити повний квадрат $(x + 1)^2 = 0$.\n\n## Приклад 3. Немає коренів\n\n$x^2 + 2x + 5 = 0$: $D = 4 - 20 = -16 \u003C 0$. Квадратний корінь з від’ємного числа серед дійсних чисел не існує — **коренів немає**.\n\n## Приклад 4. Задача з параметром (як на НМТ)\n\n> При якому значенні $a$ рівняння $x^2 - 4x + a = 0$ має рівно один корінь?\n\nОдин корінь означає $D = 0$:\n\n$$\nD = 16 - 4a = 0 \\quad\\Rightarrow\\quad a = 4\n$$\n\n**Відповідь:** $a = 4$.\n\n## Типові помилки\n\n1. **Губиться знак $b$.** Якщо $b = -5$, то $-b = 5$, а $b^2 = 25$, а не $-25$.\n2. **Ділять лише корінь на $2a$.** На $2a$ ділиться весь чисельник $-b \\pm \\sqrt{D}$.\n3. **Забувають про $a \\ne 0$.** Якщо $a = 0$, рівняння вже лінійне, і формула не працює.\n\n## Спробуйте самі\n\nРозв’яжіть $3x^2 - 7x + 2 = 0$.\n\n::answer\nВідповідь: $D = 49 - 24 = 25$, $x_1 = 2$, $x_2 = \\tfrac{1}{3}$.\n::\n",{"title":5,"description":4748},"blog\u002Fkvadratni-rivnyannya-dyskryminant",[4760,295,4761,4762],"квадратні рівняння","НМТ","алгебра","Квадратні рівняння","2k3pszcqZUElyPhpymYYhEgqeJGRuEIpmCrIzB2T9yM",[4766],{"path":4767,"title":4768,"date":4769},"\u002Fblog\u002Fliniyni-rivnyannya-7-klas","Лінійні рівняння з однією змінною, 7 клас: пояснення з прикладами","2026-10-16",1792103491839]