Question

(-2x²+3x+2)(x-4)maiior ou igual a 0

Answer 1

Equação I:

$-2x^2+3x+2\geq0\\-2x^2+4x-x+2\geq0\\-2x(x-2)-1(x-2)\geq0\\(-2x-1)(x-2)\geq0$


Equação II:

$x-4\geq0$


____-_____(-1/2)____+_____(2)___-___________-____ I
____-_____________-___________-_____(4)____+____ II
____+_____(-1/2)___-______(2)___+____(4)_____-____ I n II

$\boxed{S=\left\{x\in\mathbb{R}/x\leq-\frac{1}{2}\cup 2\leq x\leq 4\right\}}$