Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 3 x - 28 \leq 0$$
A) $[ 7 , \infty )$
B) $( - \infty , - 4 ] \cup [ 7 , \infty )$
C) $( - \infty , - 4 ]$
D) $[ - 4,7 ]$

Question

Quizplus · Accepted Answer

To solve the quadratic inequality $x^2 - 3x - 28 \leq 0$, first factor the quadratic expression. The factors of -28 that add up to -3 are -7 and 4, so the factored form is $(x - 7)(x + 4) \leq 0$. The roots of the equation are $x = 7$ and $x = -4$. To determine where the expression is less than or equal to zero, test values in each interval divided by the roots: less than -4, between -4 and 7, and greater than 7. The expression is negative (or zero) between the roots, so the solution set in interval notation is $[-4, 7]$.

Solve the Quadratic Inequality x2−3x−28≤0x ^ { 2 } - 3 x - 28 \leq 0x2−3x−28≤0

Solve the Quadratic Inequality $x ^ { 2 } - 3 x - 28 \leq 0$