Solve the inequality. Write the solution set in interval notation.
-$4 p ^ { 2 } \geq 17$
A) $\left[ - \frac { \sqrt { 17 } } { 2 } , \frac { \sqrt { 17 } } { 2 } \right]$
B) $\left( - \frac { \sqrt { 17 } } { 2 } , \frac { \sqrt { 17 } } { 2 } \right)$
C) $\left( - \infty , - \frac { \sqrt { 17 } } { 2 } \right] \cup \left[ \frac { \sqrt { 17 } } { 2 } , \infty \right)$
D) $\left( - \infty , - \frac { \sqrt { 17 } } { 2 } \right) \cup \left( \frac { \sqrt { 17 } } { 2 } , \infty \right)$

Question

Quizplus · Accepted Answer

First, divide both sides of the inequality by 4 to get $p^2 \geq \frac{17}{4}$. Taking the square root of both sides gives $p \geq \frac{\sqrt{17}}{2}$ or $p \leq -\frac{\sqrt{17}}{2}$, which means $p$ is either greater than or equal to $\frac{\sqrt{17}}{2}$ or less than or equal to $-\frac{\sqrt{17}}{2}$. This corresponds to the union of two intervals: $\left( - \infty , - \frac { \sqrt { 17 } } { 2 } \right] \cup \left[ \frac { \sqrt { 17 } } { 2 } , \infty \right)$.

Solve the Inequality 4p2≥174 p ^ { 2 } \geq 174p2≥17

Solve the Inequality $4 p ^ { 2 } \geq 17$