Question

Find the remaining zeros of the following polynomial given the P(i)=0.
x^4-8x^3+14x^2-8x+13

Answer 1

P(-i) is also zero, so (x^2+1) divided p(x).

(x^4-8x^3+14x^2-8x+13)/(x^2+1) = x^2-8x+13

So, all the roots of p(x)=0 are ±i and 4±√3