Find roots of polynomial $$ p(x) = x^5-2x^3+2x^2-x-2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6636\\[1 em]x_2 &= 1.3637\\[1 em]x_3 &= -1.7587\\[1 em]x_4 &= 0.5293+0.9882i\\[1 em]x_5 &= 0.5293-0.9882i \end{aligned} $$Explanation
Polynomial $ x^5-2x^3+2x^2-x-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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