Question

Seja 1,uma das raízes de x^3+ax^2+6x-2=0.Determije o valor de a e as demais raízes​

Answer 1

$\mathtt{{1}^{3}+a.{1}^{2}+6.1-2=0}\\\mathtt{1+a+6-2=0}\\\mathtt{a=-6+2-1}$

$\huge\boxed{\boxed{\mathtt{a=-5}}}$

$\mathtt{{x}^{3}-5{x}^{2}+6x-2=0}$

x³-5x²+6x-2|x-1

-x³+x² x²-4x+2

-4x²+6x-2

+4x²-4x

2x-2

-2x+2

0

$\mathtt{{x}^{3}-5{x}^{2}+6x-2=0}\\\mathtt{(x-1)({x}^{2}-4x+2)=0}$

$\mathtt{{x}^{2}-4x+2=0}$

$\mathtt{\Delta=16-8=8}\\\mathtt{x=\dfrac{4\pm2\sqrt{2}}{2}=2\pm\sqrt{2}}$

$\mathtt{x_{1}=2+\sqrt{2}~~x_{2}=2-\sqrt{2}}$