Предмет: Алгебра, автор: Аноним

найдите сумму корня многочлена p(x)=x^3-mx^2-4x+36 , если один из корней равен 9

Ответы

Автор ответа: Trover
0
Сначала найдём параметр m. Подставим известный корень 9 и приравняем многочлен нулю.
(9)^3-mcdot(9)^2-4cdot9+36=0\729-81m-36+36=0\81m=729\m=9
Теперь найдём корни многочлена
x^3-9x^2-4x+36=0\x^2(x-9)-4(x-9)=0\(x^2-4)(x-9)=0\x=0\x^2-4=0Rightarrow x=pm2
Сумма корней 9+2+(-2) = 9
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