Question

os numeris reais -1 e 1 sao raizes da equacao x^4 -6x^3 + 9x^2+6x-10. Quais são as outras raízes?
algm ajuda please!!​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{x^4 - 6x^3 + 9x^2 + 6x - 10 = 0}$

$\mathsf{x^4 - 6x^3 + 10x^2 - x^2 + 6x - 10 = 0}$

$\mathsf{x^2(x^2 - 6x + 10x) - (x^2 + 6x - 10) = 0}$

$\mathsf{(x^2 - 1).(x^2 - 6x + 10x) = 0}$

$\mathsf{x^2 - 1 = 0}$

$\mathsf{x^2 = 1}$

$\mathsf{x = \pm\: 1}$

$\mathsf{x^2 - 6x + 10 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-6)^2 - 4.1.10}$

$\mathsf{\Delta = 36 - 40}$

$\mathsf{\Delta = -4}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{6 \pm \sqrt{-4}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{6 + 2i}{2} = 3 + i}\\\\\mathsf{x'' = \dfrac{6 - 2i}{2} = 3 - i}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{1;-1;3 + i;3 - i\}}}}$