Question

Para quais valores inteiros a função f(x) = 3x² + 12x - 36 assume valores negativos?

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{f(x) = 3x^2 + 12x - 36}$

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

$\mathsf{\Delta = (12)^2 - 4.3.(-36)}$

$\mathsf{\Delta = 144 + 432}$

$\mathsf{\Delta = 576}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-12 \pm \sqrt{576}}{6} \rightarrow \begin{cases}\mathsf{x' = \dfrac{-12 + 24}{6} = \dfrac{12}{6} = 2}\\\\\mathsf{x'' = \dfrac{-12 - 24}{6} = \dfrac{-36}{6} = -6}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \left\{\:x \in \mathbb{R}~|-6 < x < 2\right \}}}}}$