MUODILAI KUBI, muodilai algebravii tartibi seyumi namudi akh9 + bx2 + skh -f- d = 0 -ro guyand, ki dar on a^O meboshad. Dar in muodila kh-ro bo nomalumi nav u, ki bo kh tavassuti barobarii kh = u aloqamand ast,
ivaz namuda, muodilaro ba shakli
nisbatai sodda (kanoni) tabdil dodan mumkin:
u3 + ru 4- Ya = 0.
ki dar on
V* e R ” Za* ^ a 2* be d
9 ” 27a1 Za» a ’
halli in muodilaro boshad, bo yorii formulai Kardano:
U = V —d!sh + Uu2/< + R3/at 4-
| V -ih-T/qV. + p’hr yoftan mumkin ast. Agar koeffisienthoi Muodilai kubi adadhoi haqiqi boshand, kharakteri reshahoi muodila ba alomati ifodai da/« 4* rg/p% ki dar formulai Kardano tahti reshai kvadrati meboshad, vobasta ast. Agar Ya1!* 4* R3/a7 > 0 boshad, Muodilai kubi se reshai gunogun dorad: yake az onho haqiqi, dutoi digarash adadhoi kompleksii ba hamdigar hamrohshuda (payvasta) meboshand. Agar g7/i + +r3/at — 0 boshad, hamai reshaho haqiqi va dutoi onho ba hamdigar barobarand. Agar uaA+r3/a7 < 0 boshad, muodila reshahoi haqiqii gunogun dorad. Ifodai uaL+R3/a7 az diskriminavti Muodilai kubi Z)=*—4pJ—-27q2 tanho bo zarbkunandai doimi farq mekunad.
Adabiyot: K u r o sh A. G., Kurs visshey algebri, 11 izdanie., Moskva, 1975.