Question

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

Answer 1

Solve `f(x) = x^2 - 4x - 21 <= 0`

Ans: [-3, 7]

Explanation:

First, solve `f(x) = x^2 - 4x - 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(x) <= 0` inside the closed interval [-3, 7].
The 2 critical points (-3) and (7) are included in the solution set.