Find roots of polynomial $$ p(x) = x^5-5x^2+5x-40 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 2.2163\\[1 em]x_2 &= 0.561+1.7841i\\[1 em]x_3 &= 0.561-1.7841i\\[1 em]x_4 &= -1.6692+1.5407i\\[1 em]x_5 &= -1.6692-1.5407i \end{aligned} $$Explanation
Polynomial $ x^5-5x^2+5x-40 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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