Find roots of polynomial $$ p(x) = x^5-x^4+5x^3-2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.7464\\[1 em]x_2 &= -0.4027+0.5991i\\[1 em]x_3 &= -0.4027-0.5991i\\[1 em]x_4 &= 0.5296+2.2051i\\[1 em]x_5 &= 0.5296-2.2051i \end{aligned} $$Explanation
Polynomial $ x^5-x^4+5x^3-2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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