Find roots of polynomial $$ p(x) = z^5-4z^4-3z^3-4 $$
Answer
The roots of polynomial $ p(z) $ are:
$$ \begin{aligned}z_1 &= 4.6532\\[1 em]z_2 &= 0.5343+0.7075i\\[1 em]z_3 &= 0.5343-0.7075i\\[1 em]z_4 &= -0.8609+0.5937i\\[1 em]z_5 &= -0.8609-0.5937i \end{aligned} $$Explanation
Polynomial $ z^5-4z^4-3z^3-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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