Cya stattya potrebuye dodatkovih posilan na dzherela dlya polipshennya yiyi perevirnosti Bud laska dopomozhit udoskonaliti cyu stattyu dodavshi posilannya na nadijni avtoritetni dzherela Zvernitsya na storinku obgovorennya za poyasnennyami ta dopomozhit vipraviti nedoliki Material bez dzherel mozhe buti piddano sumnivu ta vilucheno 16 chervnya 2022 Diskrimina nt vi rizhnik 1 vid lat discriminar rozbirati rozriznyati mnogochlena p x a 0 a 1 x a n x n displaystyle p x a 0 a 1 x a n x n za viznachennyam ce dobutok D p a n 2 n 2 i lt j a i a j 2 displaystyle D p a n 2n 2 prod i lt j alpha i alpha j 2 de a 1 a 2 a n displaystyle alpha 1 alpha 2 alpha n vsi koreni z urahuvannyam kratnostej v deyakomu rozshirenni osnovnogo polya v yakomu voni isnuyut Vlastivosti RedaguvatiDiskriminant rivnij nulyu t i t t koli mnogochlen maye kratni koreni Diskriminant ye simetrichnim mnogochlenom shodo koreniv mnogochlena i tomu ye mnogochlenom vid jogo koeficiyentiv ba bilshe koeficiyenti cogo mnogochlena cili tomu ne zalezhat vid rozshirennya v yakomu berutsya koreni D p 1 n n 1 2 a n R p p displaystyle D p frac 1 n n 1 2 a n R p p nbsp de R p p displaystyle R p p nbsp rezultant mnogochlena p x displaystyle p x nbsp i jogo pohidnoyi p x displaystyle p x nbsp Zokrema diskriminant mnogochlena p x x n a n 1 x n 1 a 1 x a 0 displaystyle p x x n a n 1 x n 1 ldots a 1 x a 0 nbsp rivnij z tochnistyu do znaku viznachnikovi takoyi matrici 1 a n 1 displaystyle a n 1 nbsp a n 2 displaystyle a n 2 nbsp a 0 displaystyle a 0 nbsp 0 00 1 a n 1 displaystyle a n 1 nbsp a n 2 displaystyle a n 2 nbsp a 0 displaystyle a 0 nbsp 0 00 0 1 a n 1 displaystyle a n 1 nbsp a n 2 displaystyle a n 2 nbsp a 0 displaystyle a 0 nbsp 0 0 0 0 0 0 0 1 a n 1 displaystyle a n 1 nbsp a n 2 displaystyle a n 2 nbsp a 0 displaystyle a 0 nbsp n displaystyle n nbsp n 1 a n 1 displaystyle n 1 a n 1 nbsp n 2 a n 2 displaystyle n 2 a n 2 nbsp a 1 displaystyle a 1 nbsp 0 0 00 n displaystyle n nbsp n 1 a n 1 displaystyle n 1 a n 1 nbsp n 2 a n 2 displaystyle n 2 a n 2 nbsp a 1 displaystyle a 1 nbsp 0 0 00 0 n displaystyle n nbsp n 1 a n 1 displaystyle n 1 a n 1 nbsp n 2 a n 2 displaystyle n 2 a n 2 nbsp a 1 displaystyle a 1 nbsp 0 0 0 0 0 0 0 0 n displaystyle n nbsp n 1 a n 1 displaystyle n 1 a n 1 nbsp n 2 a n 2 displaystyle n 2 a n 2 nbsp a 1 displaystyle a 1 nbsp 00 0 0 0 0 0 n displaystyle n nbsp n 1 a n 1 displaystyle n 1 a n 1 nbsp n 2 a n 2 displaystyle n 2 a n 2 nbsp a 1 displaystyle a 1 nbsp Primitki Redaguvati Reyestr represovanih sliv Arhiv originalu za 4 sichnya 2019 Prikladi RedaguvatiDiskriminant kvadratnogo trichlena a x 2 b x c displaystyle ax 2 bx c nbsp dorivnyuye b 2 4 a c displaystyle b 2 4ac nbsp Diskriminant mnogochlena a 3 x 3 a 2 x 2 a 1 x a 0 displaystyle a 3 x 3 a 2 x 2 a 1 x a 0 nbsp dorivnyuye4 a 1 3 a 3 a 1 2 a 2 2 4 a 0 a 2 3 18 a 0 a 1 a 2 a 3 27 a 0 2 a 3 2 displaystyle 4a 1 3 a 3 a 1 2 a 2 2 4a 0 a 2 3 18a 0 a 1 a 2 a 3 27a 0 2 a 3 2 nbsp Zokrema diskriminant mnogochlena x 3 p x q displaystyle x 3 px q nbsp koreni yakogo obchislyuyetsya za formuloyu Kardano dorivnyuye 27 q 2 4 p 3 displaystyle 27q 2 4p 3 nbsp Otrimano z https uk wikipedia org w index php title Diskriminant amp oldid 39613071
