Solve the problem.
-$x ^ { 2 } - 3 x \geq - 2$
A) $( - \infty , 1 ]$ or $[ 2 , \infty )$
B) $[ 1,2 ]$
C) $[ 2 , \infty )$
D) $( - \infty , 1 ]$

Question

Quizplus · Accepted Answer

First, rearrange the inequality to $x^2 - 3x + 2 \geq 0$. Factoring gives $(x - 1)(x - 2) \geq 0$. The critical points are x = 1 and x = 2. Testing intervals around these points shows that the inequality holds for $x \leq 1$ and $x \geq 2$, hence the solution is $(-\infty, 1]$ or $[2, \infty)$.

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Solve the Problem $x ^ { 2 } - 3 x \geq - 2$