Find roots of polynomial $$ p(x) = x^6+2x^5-4x^3+2x^2+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.0181+0.4997i\\[1 em]x_2 &= 1.0181-0.4997i\\[1 em]x_3 &= -0.28+0.8079i\\[1 em]x_4 &= -0.28-0.8079i\\[1 em]x_5 &= -1.7381+1.1106i\\[1 em]x_6 &= -1.7381-1.1106i \end{aligned} $$Explanation
Polynomial $ x^6+2x^5-4x^3+2x^2+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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