Final answer:
The given polynomial function f(x) = x⁴ - 4x³ + 4x² is a fourth-degree polynomial function. Its solutions are x = 0 (with multiplicity 2) and x = 2 (with multiplicity 2).
Step-by-step explanation:
The given polynomial function is f(x) = x⁴ - 4x³ + 4x². This is a fourth-degree polynomial function. To solve it, we can look for the roots or zeros of the polynomial. We can factor it as f(x) = x²(x - 2)², which means x = 0 is a root of multiplicity 2 and x = 2 is a root of multiplicity 2. Therefore, the solutions to the equation f(x) = 0 are x = 0 (with multiplicity 2) and x = 2 (with multiplicity 2).