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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.

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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 $x$

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  • $\begingroup$ So this is just an expression of the quadratic type and I should treat it as such? $\endgroup$ – Cherry_Developer Sep 22 '14 at 23:39
  • $\begingroup$ yes kind of... but when you do the factorization for $u$ you have to remember to go back to $x$ $\endgroup$ – Jearson Narvaez Rojas Sep 22 '14 at 23:40
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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

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