Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 4 x - 21 \leq 0$$
A) $( - \infty , - 3 ] \cup [ 7 , \infty )$
B) $[ 7 , \infty )$
C) $( - \infty , - 3 ]$
D) $[ - 3,7 ]$

Question

Quizplus · Accepted Answer

First, factor the quadratic inequality: $x^2 - 4x - 21 = (x - 7)(x + 3) \leq 0$. The roots are $x = 7$ and $x = -3$. The inequality is satisfied between these two roots, including the roots themselves, hence the solution is $[ - 3,7 ]$.

Solve the Inequality x2−4x−21≤0x ^ { 2 } - 4 x - 21 \leq 0x2−4x−21≤0

Solve the Inequality $x ^ { 2 } - 4 x - 21 \leq 0$