Find roots of polynomial $$ p(x) = x^5+41x^4+432x^3+1650x^2+2600x+1000 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5508\\[1 em]x_2 &= -8.0487\\[1 em]x_3 &= -27.2362\\[1 em]x_4 &= -2.5822+1.2704i\\[1 em]x_5 &= -2.5822-1.2704i \end{aligned} $$Explanation
Polynomial $ x^5+41x^4+432x^3+1650x^2+2600x+1000 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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