Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } - 10 x - 24 \leq 0$$
A) $( - \infty , 4 ] \cup [ 6 , \infty )$
B) $( - \infty , \infty )$
C) $( - \infty , - 4 ] \cup [ 6 , \infty )$
D) $( - \infty , - 6 ] \cup [ - 4 , \infty )$

Question

Quizplus · Accepted Answer

To solve the inequality $- x ^ { 2 } - 10 x - 24 \leq 0$, we first find the roots of the equation $- x ^ { 2 } - 10 x - 24 = 0$. Factoring or using the quadratic formula, we find the roots to be $x = -6$ and $x = -4$. Since the leading coefficient is negative, the parabola opens downwards, meaning the inequality is satisfied between the roots. Thus, the solution in interval notation is $( - \infty , - 6 ] \cup [ - 4 , \infty )$.

Solve the Inequality −x2−10x−24≤0- x ^ { 2 } - 10 x - 24 \leq 0−x2−10x−24≤0

Solve the Inequality $- x ^ { 2 } - 10 x - 24 \leq 0$