Question

How do you find the real zeros and their multiplicity of f(x)=-x^5+5x^4+4x^3-20x^2?

Answer 1

Factor: - x^2(x^3 - 5x^2 - 4x + 20)=
- x^2 [x^2(x - 5) - 4(x - 5)] = factoring by grouping
- x^2 (x^2 - 4)(x - 5) = by grouping
- x^2 (x + 2)(x - 2) (x - 5) refactoring x^2 - 4 as difference of squares
Set each factor equal to zero, you get x = 0, x = -2, x = 2, and x = 5

Zero has a multiplicity of two.