What is the complete solution set of the function including multiplcity?

Question

f(x)=x⁴-256

and please explain too!

Answer 1

By "solution set", I assume that you mean: the values of x for which f(x) = 0

x⁴ - 256 = 0

(x²)² - (16)² = 0

(x² - 16)(x² + 16) = 0

(x + 4)(x - 4)(x² + 16) = 0

x = 4, -4, or x² = -16

x = 4, -4, 4i, -4i (each solution has multiplicity one)