Use algebraic and/or graphical methods to solve the inequality.
- $m ^ { 3 } - 25 m \geq 0$

Question

Use algebraic and/or graphical methods to solve the inequality. -$$m ^ { 3 } - 25 m \geq 0$$ A) $- 5 < x \leq 0$ or $x \geq 5$ B) $- 5 < x < 0$ or $x > 5$ C) $- 5 \leq x \leq 0$ or $x \geq 5$ D) $- 5 \leq x < 0$ or $x > 5$

Quizplus · Accepted Answer

First, factor the inequality: $m^3 - 25m = m(m^2 - 25) = m(m - 5)(m + 5) \geq 0$. The roots are $m = 0$, $m = 5$, and $m = -5$. Testing intervals around these roots shows that the inequality holds for $m \leq -5$, $0 \leq m \leq 5$, and $m \geq 5$. Thus, the correct answer is $m \leq -5$, $0 \leq m \leq 5$, or $m \geq 5$, which corresponds to option C: $- 5 \leq x \leq 0$ or $x \geq 5$.

Use Algebraic And/or Graphical Methods to Solve the Inequality m3−25m≥0m ^ { 3 } - 25 m \geq 0m3−25m≥0

Use Algebraic And/or Graphical Methods to Solve the Inequality $m ^ { 3 } - 25 m \geq 0$