Find roots of polynomial $$ p(x) = 2x^5+27x^4+144x^3+391x^2+492x+180 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5862\\[1 em]x_2 &= -2.4473\\[1 em]x_3 &= -5.4643\\[1 em]x_4 &= -2.5012+2.2861i\\[1 em]x_5 &= -2.5012-2.2861i \end{aligned} $$Explanation
Polynomial $ 2x^5+27x^4+144x^3+391x^2+492x+180 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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