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I'm asked questions like to find the zeros, and multplicities of the $\mathbb{C}$-polynomials

$f(z) =z^6 +4z^2 - 1 \hspace{10mm} , |z| < 1$ or worse yet $f(z)=z^{87}+36z^{57}+71z^4+z^3-z+1 \hspace{10mm}, 1<|z|<2$

Surely factoring these things isn't the right approach...and I can't seem to think of a way to find them otherwise? We've been looking at some nice things we can do if we know what the zeros/singularities are, but as for finding them.. I don't know.

Thanks for any push in the right direction!

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    @Chloe.H You're absolutely right: you shouldn't, and most likely can't, factorise them. The Abel–Ruffini theorem tells us that there is no general algebraic solution to polynomial equations of degree five or higher. – 2012-11-20

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