Solve the inequality. Use algebra to solve the corresponding equation.
-$$x ^ { 2 } - 8 x + 15 \geq 0$$
A) $[ 3,5 ]$
B) $[ 5 , \infty )$
C) $( - \infty , 3 ]$
D) $( - \infty , 3 ] \cup [ 5 , \infty )$

Question

Quizplus · Accepted Answer

First, solve the equation $x^2 - 8x + 15 = 0$ by factoring: $(x - 3)(x - 5) = 0$, which gives roots $x = 3$ and $x = 5$. These divide the number line into three intervals: $(-\infty, 3)$, $(3, 5)$, and $(5, \infty)$. Testing values from each interval in the inequality $x^2 - 8x + 15 \geq 0$ shows that the inequality holds for $x$ values in the intervals $(-\infty, 3]$ and $[5, \infty)$.

Solve the Inequality x2−8x+15≥0x ^ { 2 } - 8 x + 15 \geq 0x2−8x+15≥0

Solve the Inequality $x ^ { 2 } - 8 x + 15 \geq 0$