Question

A função y = – x² + 5x – 4 será positiva quando? { x ∈ R | x 4} { x ∈ R | 1 > x} { x ∈ R | 1 4} { x ∈ R | 1 4}

Answer 1

Explicação passo-a-passo:

$\sf -x^2+5x-4 > 0$

$\sf \Delta=5^2-4\cdot(-1)\cdot(-4)$

$\sf \Delta=25-16$

$\sf \Delta=9$

$\sf x=\dfrac{-5\pm\sqrt{9}}{2\cdot(-1)}=\dfrac{-5\pm3}{-2}$

$\sf x'=\dfrac{-5+3}{-2}~\Rightarrow~x'=\dfrac{-2}{-2}~\Rightarrow~x'=1$

$\sf x'=\dfrac{-5-3}{-2}~\Rightarrow~x"=\dfrac{-8}{-2}~\Rightarrow~x"=4$

$\sf \red{S=\{x\in\mathbb{R}~|~1 < x < 4\}}$