I need to find all roots of the polynomial Px x58x2 I need t

I need to find all roots of the polynomial P(x)= -x^5+8x^2. I need to know the steps for the assignment to show proof I comprehend. Plus I need to know how to teach it.

Solution

Given P(x)=-x^5 + 8x^2

for roots of polynomial, P(x) we have now

P(x)=-x^5 + 8x^2=0

Or, x^5 - 8x^2=0

Or, x^2(x^3 - 8)=0

Or, x^2 (x-2)(x^2 +2x+4)=0

So either x^2=0; x-2=0; (x^2 + 2x +4)=0

So, x=0; x=2 are the ral roots

and for (x^2 + 2x +4)=0 roots are imaginary

Therfore x= -1- i sqrt(3) and x= -1+ i sqrt(3)