Question

Approximate the real number solution(s) to the polynomial function f(x) = x3 + 2x2 − 5x − 6.

a. x = −3, x = −1, x = 2

b. x = 3, x = 1, x = −2

c.x = 3, x = −1, x = 2

d.x = −3, x = 1, x = −2

Answer 1

f(1) = (1)^3 + 2(1)^2 - 5(1) - 6 = 1 + 2 - 5 - 6 = -8; x = 1 is not a solution to the polynomial.
f(-1) = (-1)^3 + 2(-1)^2 - 5(-1) - 6 = -1 + 2 + 5 - 6 = 0; x = -1 is a solution to polynomial.
From the options, a or c has x = -1, both has x = , so lets check for x = 3
f(3) = (3)^3 + 2(3)^2 - 5(3) - 6 = 27 + 18 - 15 - 6 = 24; x = 3 is not a solution to the polynomial.
Therefore the solutions to the polynomial are x = -3, x = -1, x = 2