Question

When is -2x^3-13x^2+8x+52 ≥ 0?

Answer 1

x ≤ -13/2 ∨ -2≤ x ≤ 2

Explanation:

-x²(2x + 13) + 4(2x+ 13) ≥ 0

(2x+13)(-x²+4) ≥ 0

(2x+13)(2+x)(2-x) ≥ 0

2x + 13 ≥ 0

2x ≥ -13

2/2 x ≥ -13/2

x ≥ -13/2

2+ x ≥ 0

x ≥ -2

2 - x ≥ 0

-x ≥ -2

x ≤ 2

-13/2. -2. 2

- +. +. +

- - +. +

+. +. +. -

+. - +. -

x ≤ -13/2 ∨ -2≤ x ≤ 2