Find roots of polynomial $$ p(x) = 180x^5+60x^3+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.3862\\[1 em]x_2 &= 0.277+0.3269i\\[1 em]x_3 &= 0.277-0.3269i\\[1 em]x_4 &= -0.0839+0.6204i\\[1 em]x_5 &= -0.0839-0.6204i \end{aligned} $$Explanation
Polynomial $ 180x^5+60x^3+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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