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I'm having trouble figuring out to find the complex roots of polynomials with degree greater than 2.

I particular, how would I find the (complex) roots of the following: $$x^4 + 5x^2 +4?$$ I know the roots are $\pm i$, $\pm2i$, but for the life of me I cannot figure out how I would determine this if I didn't already know.

Your help would be greatly appreciated!

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Hint: Subsitute $w=x^2$ and observe that you get a quadratic equation in $w$. Now you can solve it for $w$, substitute back for $x^2$, and solve for $x$.

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Thanks, Clayton. You're a genius! :) – Matthew Jan 24 '13 at 4:30
@Matthew: I wouldn't go as far as to say that, but thanks for the compliment. I'm glad it helped. – Clayton Jan 24 '13 at 4:31

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