Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the following conditions

Question

Zero of 0 and zero of 2 having multiplicity 2; f(3)=18

Answer 1

A zero of 0 means there is a common x factor

A zero of 2 means there is a factor of (x -2) , and " multiplicity of 2" means there are 2 of them.

So:

f(x) = x*(x - 2)*(x - 2) = x³ - 4x² + 4x

f(3) = 27 - 36 + 12 = 3, so we need to multiply by 6 to get 18:

f(x) = 6x³ - 24x² + 24x

Answer 2

f(x) = Ax(x - 2)²

18 = A(3)(3 - 2)² = 3A

A = 6

f(x) = 6x(x - 2)²