Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 7 x \leq - 12$$
A) $( - \infty , 3 ] \cup [ 4 , \infty )$
B) $[ 3,4 ]$
C) $[ - 4 , - 3 ]$
D) $( 3,4 )$

Question

Quizplus · Accepted Answer

First, rearrange the inequality to standard form: $x^2 + 7x + 12 \leq 0$. Factoring gives $(x + 3)(x + 4) \leq 0$. The critical points are $x = -3$ and $x = -4$. Testing intervals shows that the inequality holds for $x$ in the interval $[-4, -3]$.

Solve the Quadratic Inequality x2+7x≤−12x ^ { 2 } + 7 x \leq - 12x2+7x≤−12

Solve the Quadratic Inequality $x ^ { 2 } + 7 x \leq - 12$