Question

Find the polynomial function with the following roots: -2 of multiplicity 2; and 3.

SHOW WORK (DBA questions of module 4)

Answer 1

f(x) = x³ + x² - 8x - 12

Explanation:

given roots x = -2 of multiplicity 2 and x = 3, then

(x + 2)² and (x - 3) are factors and the polynomial is the product of the factors

f(x) = a(x + 2)²(x - 3) ← where a is a multiplier

f(x) = (x² + 4x + 4)(x - 3) ← with a = 1

= x³ + x² - 8x - 12