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

SHOW WORK (DBA questions of module 4)

f (x) = x³ + x² - 8x - 12

Step-by-step 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