Question

Solve each quadratic inequality then test their interval of the inequality.

1. x² - x - 20 > 0
2. x² - 2x - 11 < 0
3. x²+ 9x + 14 > 0
4. r² - 10r + 16 > 0​

Answer 1

Explanation:

1) x² -x - 20 > 0

x² - 5x + 4x - 20 > 0

x( x - 5) + 4(x - 5) > 0

(x - 5)(x + 4) > 0

x - 5 > 0 ; x + 4> 0

x > 5 ; x < -4

3) x² + 9x + 14 > 0

x² + 7x + 2x + 14 > 0

x(x + 7) + 2(x + 7) > 0

(x + 7) (x + 2) > 0

x < - 7 and x > -2

4) r² - 10r + 16 > 0

r² - 8r -2r + 16 > 0

r(r - 8) - 2(r - 8) > 0

(r - 8)(r - 2) > 0

r < 2 ; r > 8