Solve and graph the inequality: x^3-2x^2-9x-2≥-20 give solution in interval notation

Answer 1

x^3-2x^2-9x-2≥-20

x^3-2x^2-9x+18≥0

(x-2)(x^2-9) >= 0

(x-2)(x-3)(x+3)>= 0

Roots are -3, 2, and 3, and the leading coefficient is positive. Since all roots are single roots, the signs alternate, and the function is nonnegative on [3, ∞)

Thus,

[-3, 2] ∪ [3, ∞)