Find a polynomial function

Question

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

Zero of 0 and Zero of 1 have multiplicity 2; f(2)=10

Answer 1

I assume you meant to say that the zero of 1 has multiplicity of 2.

f(x) = ax(x - 1)²

f(2) = 10 ⇒

a(2)(2 - 1)² = 10

a = 5

f(x) = 5x(x - 1)²

Test the answer.