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

Question

Quizplus · Accepted Answer

To solve the inequality $x^2 - 5x \leq 0$, factor out $x$ to get $x(x - 5) \leq 0$. This implies that the product of $x$ and $x-5$ is non-positive, meaning either both are non-positive or one is non-positive and the other is non-negative. The critical points are $x = 0$ and $x = 5$, which divide the number line into intervals. Testing values in each interval shows that the inequality holds for $x$ in the interval $[0, 5]$.

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

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