$x ^ { 3 } + 10 x ^ { 2 } + 31 x \leq - 30$
A) $- 5 \leq x \leq - 3 \text { or } x \geq - 2$
B) $x

Question

$x ^ { 3 } + 10 x ^ { 2 } + 31 x \leq - 30$
A) $- 5 \leq x \leq - 3 \text { or } x \geq - 2$
B) $x < - 5 \text { or } - 3 < x < - 2$
C) $x \leq 2 \text { or } 3 \leq x \leq 5$
D) $x \leq - 5 \text { or } - 3 \leq x \leq - 2$

Quizplus · Accepted Answer

First, factor the given inequality: $x^3 + 10x^2 + 31x + 30 \leq 0$. Factoring gives $(x + 2)(x + 3)(x + 5) \leq 0$. The roots are $x = -5, -3, -2$. Testing intervals around these roots shows that the inequality holds for $x \leq -5$ and $-3 \leq x \leq -2$.

x3+10x2+31x≤−30x ^ { 3 } + 10 x ^ { 2 } + 31 x \leq - 30x3+10x2+31x≤−30

$x ^ { 3 } + 10 x ^ { 2 } + 31 x \leq - 30$