Find roots of polynomial $$ p(x) = -x^5+x^2+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.298\\[1 em]x_2 &= 0.2346+1.0016i\\[1 em]x_3 &= 0.2346-1.0016i\\[1 em]x_4 &= -0.8837+0.8217i\\[1 em]x_5 &= -0.8837-0.8217i \end{aligned} $$Explanation
Polynomial $ -x^5+x^2+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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