Для уравнения nx2 + 6x + m = 0 определи значения n и m, если известны решения ур...

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August 2022 1 8 Report

Для уравнения nx2 + 6x + m = 0 определи значения n и m, если известны решения уравнения x = 2 и x = –1.
n=
m=

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natalijawirt

Ответ:

$n=-6$

$m=12$

Объяснение:

Согласно теореме Виета: Для произвольного квадратного уравнения $ax^{2} +bx+c=0$ :

$x_{1} +x_{2} =\frac{-b}{a} \\x_{1} *x_{2} =\frac{c}{a}$

Тогда:

$2+(-1)=\frac{-6}{n} \\2*(-1) =\frac{m}{n}$

$1=\frac{-6}{n} \\-2 =\frac{m}{n}$

Найдем n

$1=\frac{-6}{n} \\ 1=-6:n\\n=-6:1\\n=-6$

И m :

$-2 =\frac{m}{n}\\-2 =\frac{m}{-6}\\-2=m:(-6)\\m=(-2)*(-6)\\m=12$

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