Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 6 x + 5 \geq 0$$
A) $( - \infty , - 5 ] \cup [ - 1 , \infty )$
B) $( - \infty , - 5 ]$
C) $[ - 1 , \infty )$
D) $[ - 5 , - 1 ]$

Question

Quizplus · Accepted Answer

To solve the quadratic inequality $x^2 + 6x + 5 \geq 0$, first factor the quadratic expression. It factors as $(x + 5)(x + 1) \geq 0$. The roots are $x = -5$ and $x = -1$. To determine where the expression is non-negative, test intervals around the roots: less than -5, between -5 and -1, and greater than -1. The expression is non-negative outside the interval $(-5, -1)$, thus the solution set is $(-\infty, -5] \cup [-1, \infty)$.

Solve the Quadratic Inequality x2+6x+5≥0x ^ { 2 } + 6 x + 5 \geq 0x2+6x+5≥0

Solve the Quadratic Inequality $x ^ { 2 } + 6 x + 5 \geq 0$