Question

what is the solution set of the quadratic inequality $x^2 + x - 2 geq 0$?
○ ${x | x leq -2 \text{ or } x geq 1}$
○ ${x | x leq -1 \text{ or } x geq 2}$
○ ${x | x geq -2 \text{ or } x leq 1}$
○ ${x | x geq -1 \text{ or } x leq 2}$

Explanation:

Step1: Factor the quadratic expression

$x^2 + x - 2 = (x + 2)(x - 1)$

Step2: Find critical points

Set $(x + 2)(x - 1) = 0$, so $x = -2$ or $x = 1$.

Step3: Test intervals

• For $x < -2$: $(x+2)<0, (x-1)<0$, product $>0$ (satisfies $\geq0$)
• For $-2 < x < 1$: $(x+2)>0, (x-1)<0$, product $<0$ (does not satisfy)
• For $x > 1$: $(x+2)>0, (x-1)>0$, product $>0$ (satisfies $\geq0$)

Include critical points since inequality is $\geq0$.

Answer:

A. $\{x| x\leq-2 \text{ or } x\geq 1\}$