Find roots of polynomial $$ p(x) = z^4-4z^3+14z^2-4z+13 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= i\\[1 em]z_2 &= -i\\[1 em]z_3 &= 2+3i\\[1 em]z_4 &= 2-3i \end{aligned} $$Explanation
Polynomial $ z^4-4z^3+14z^2-4z+13 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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