Solve the polynomial inequality. Write the answer in interval notation. $$2 x ^ { 2 } - 17 x \leq - 21$$
A) $\left[ \frac { 3 } { 2 } , 7 \right]$
B) $\left( - \infty , \frac { 3 } { 2 } \right) \cup ( 7 , \infty )$
C) $\left[ - 7 , - \frac { 3 } { 2 } \right]$
D){ }

Question

Solve the polynomial inequality. Write the answer in interval notation. $$2 x ^ { 2 } - 17 x \leq - 21$$
A) $\left[ \frac { 3 } { 2 } , 7 \right]$
B) $\left( - \infty , \frac { 3 } { 2 } \right) \cup ( 7 , \infty )$
C) $\left[ - 7 , - \frac { 3 } { 2 } \right]$
D){  }

Quizplus · Accepted Answer

First, rearrange the inequality to standard form: $2x^2 - 17x + 21 \leq 0$. Factoring gives $(2x - 3)(x - 7) \leq 0$, which has roots $x = \frac{3}{2}$ and $x = 7$. The inequality is satisfied between these roots, including the endpoints, hence $\left[ \frac { 3 } { 2 } , 7 \right]$.

Solve the Polynomial Inequality 2x2−17x≤−212 x ^ { 2 } - 17 x \leq - 212x2−17x≤−21

Solve the Polynomial Inequality $2 x ^ { 2 } - 17 x \leq - 21$