Find roots of polynomial $$ p(x) = 5x^5-x^4+25x^2+2x-50 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2114\\[1 em]x_2 &= 0.8634+1.7347i\\[1 em]x_3 &= 0.8634-1.7347i\\[1 em]x_4 &= -1.3691+0.5695i\\[1 em]x_5 &= -1.3691-0.5695i \end{aligned} $$Explanation
Polynomial $ 5x^5-x^4+25x^2+2x-50 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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