Solve the inequality.
-$x ^ { 2 } - 5 x \leq 0$
A) $( - \infty , 0 ]$ or $[ 5 , \infty )$
B) $[ 0,5 ]$
C) $[ - 5,0 ]$
D) $( - \infty , - 5 ]$ or $[ 0 , \infty )$

Question

Quizplus · Accepted Answer

To solve the inequality $x^2 - 5x \leq 0$, factor out an $x$ to get $x(x - 5) \leq 0$. This implies that the product of $x$ and $x-5$ is non-positive, meaning $x$ is in the interval where it changes sign at the roots $0$ and $5$. By testing values or using a sign chart, we find that the inequality holds for $x$ in the interval $[0, 5]$.

Solve the Inequality x2−5x≤0x ^ { 2 } - 5 x \leq 0x2−5x≤0

Solve the Inequality $x ^ { 2 } - 5 x \leq 0$