I'm looking for the polynomial function

Question

Polynomial function f(x) of degree 3 with real coefficients that satisfies, Zero of 0 and zero of 1 having multiplicity 2; f(2)=12.

Answer 1

f(x) = Ax(x - 1)²

where A is real and A ≠ 0. Now set

f(2) = 12

and solve for A. You should be able to finish from here.