Solve the inequality. Write the solution set in interval notation.
- $- 2 x ^ { 2 } + 5 x \geq 0$
A) $\left( - \infty , - \frac { 5 } { 2 } \right] \cup [ 0 , \infty )$
B) $\left[ - \frac { 5 } { 2 } , 0 \right]$
C) $( - \infty , 0 ] \cup \left[ \frac { 5 } { 2 } , \infty \right]$
D) $\left[ 0 , \frac { 5 } { 2 } \right]$

Question

Solve the inequality. Write the solution set in interval notation.
-  $- 2 x ^ { 2 } + 5 x \geq 0$
A) $\left( - \infty , - \frac { 5 } { 2 } \right] \cup [ 0 , \infty )$
B) $\left[ - \frac { 5 } { 2 } , 0 \right]$
C) $( - \infty , 0 ] \cup \left[ \frac { 5 } { 2 } , \infty \right]$
D) $\left[ 0 , \frac { 5 } { 2 } \right]$

Quizplus · Accepted Answer

To solve the inequality $-2x^2 + 5x \geq 0$, factor out an $x$ to get $x(-2x + 5) \geq 0$. The roots of the equation are $x = 0$ and $x = \frac{5}{2}$. Since the coefficient of $x^2$ is negative, the parabola opens downwards, meaning the expression is non-negative between its roots. Thus, the solution in interval notation is $[0, \frac{5}{2}]$.

Solve the Inequality −2x2+5x≥0- 2 x ^ { 2 } + 5 x \geq 0−2x2+5x≥0

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