Question

equação do segundo grau x²-x-42=0​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{x^2 - x - 42 = 0}$

$\sf{x^2 - x -6x + 6x - 42 = 0}$

$\sf{x^2 - 7x + 6x - 42 = 0}$

$\sf{x(x - 7) + 6(x - 7) = 0}$

$\sf{(x + 6)\:.\:(x - 7) = 0}$

$\boxed{\boxed{\sf{S = \{7,-6\}}}}$

$\textsf{Ou}$

$\sf{ax^2 + bx + c = 0}$

$\sf{x^2 - x - 42 = 0}$

$\sf{a = 1\:\:\:\:\:b = -1\:\:\:\:\:c = -42}$

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

$\sf{\Delta = (-1)^2 - 4.1.(-42)}$

$\sf{\Delta =1 + 168}$

$\sf{\Delta = 169}$

$\sf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{169}}{2} \rightarrow \begin{cases}\sf{x' = \dfrac{1 + 13}{2} = \dfrac{14}{2} = 7}\\\\\sf{x'' = \dfrac{1 - 13}{2} = -\dfrac{12}{2} = -6}\end{cases}}$

$\boxed{\boxed{\sf{S = \{7,-6\}}}}$