Stuck finding the zeros of a polynomial (complex and real)

Question

Stuck finding the zeros of this polynomial (complex and real): $$x^4+2x^2+1$$

I am not sure how I would factor this. The constant value is really throwing me off. I just need a hint on how to get that done and I think I have a handle on the rest of it.

Answer 1

set $u = x^2$ and use the quadratic formula to factorize it.

if you do the change, you will have

$u^2 +2u +1$ and from here its easy to solve it, ones you factorize it remember to go back to $x$

Answer 2

set $u = x^2$ and use the quadratic formula to factorize it.

if you do the chage, you will have

$u^2 +2u +1$ and from here its easy to solve it.

$$u^2 +2u +1 = (u+1)(u+1) = (x^2 +1)(x^2 +1) = (x-i)(x+i)(x-i)(x+i) =(x-i)^{2}(x+i)^{2}$$ and its done