Find roots of polynomial $$ p(x) = 10x^5+2x^3+x+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.833\\[1 em]x_2 &= 0.7026+0.58i\\[1 em]x_3 &= 0.7026-0.58i\\[1 em]x_4 &= -0.2861+0.8866i\\[1 em]x_5 &= -0.2861-0.8866i \end{aligned} $$Explanation
Polynomial $ 10x^5+2x^3+x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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