Answer:
f(x) = [tex]x^{4}[/tex] - 2x³ - 11x² + 12x + 36
Step-by-step explanation:
given that x = a and x = b are the roots of a polynomial then
(x - a) and (x - b) are it's factors and the polynomial is the product of the factors
here x = -2 ( repeated ) and x = 3 (repeated), hence the factors are
(x + 2)² and (x - 3)² → the square denotes a repeated root
f(x) = (x + 2)²(x - 3)² ← expand factors and simplify
= (x² + 4x + 4)(x² - 6x +9)
= [tex]x^{4}[/tex] - 2x³ - 11x² + 12x + 36 ← is a possible equation
