Find all zeros to the following polynomial function. f(x)= 5x^4 -10x^3 +4x^2 -8x. Please answer in detailed steps I’m confused.

Please check the explanation.

Step-by-step explanation:

Given the function

To determine the zeros, set f(x) = 0

switch sides

as

so the equation becomes

Using the zero factor principle:

so solving

Therefore, the real zeros are:

and

has all the imaginary zeros.

solving

      ∵

Therefore, the total zeros are:

step-by-step explanation: