# How do you solve x^2 - 4x - 21<=0 A) [-3, 7] B) (-∞, -3] C) (-∞, -3] [7, ∞) D) [7, ∞)?

Aug 16, 2015

Solve $f \left(x\right) = {x}^{2} - 4 x - 21 \le 0$

Ans: [-3, 7]

#### Explanation:

First, solve $f \left(x\right) = {x}^{2} - 4 x - 21 = 0$Roots have opposite signs.
Factor pairs of (-21) --> (-3, 7). This sum is 4 = -b. Then, the 2 real roots are: -3 and 7.
Between the 2 real roots (-3) and (7), f(x) has the opposite sign of a = 1. Then $f \left(x\right) \le 0$ inside the closed interval [-3, 7].
The 2 critical points (-3) and (7) are included in the solution set.