Question

Quais são as raízes reais da equação x² – x -6=0? *
A) X'=3 E X''= 2
B) X'= -3 E X''= -2
C) X'= 3 E X''= -2
D) X'= -3 E X''= 2.
$x$
​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

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

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

$\mathsf{\Delta = (-1)^2 - 4.1.(-6)}$

$\mathsf{\Delta = 1 + 24}$

$\mathsf{\Delta = 25}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{25}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{1 + 5}{2} = \dfrac{6}{2} = 3}\\\\\mathsf{x'' = \dfrac{1 - 5}{2} = \dfrac{-4}{2} = -2}\end{cases}}$

$\boxed{\boxed{\textsf{S = \{3;-2\}}}}\leftarrow\textsf{letra C}$