Find roots of polynomial $$ p(x) = -x^6+x^3+4x^2+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.3394\\[1 em]x_2 &= 1.5633\\[1 em]x_3 &= 0.0322+0.4987i\\[1 em]x_4 &= 0.0322-0.4987i\\[1 em]x_5 &= -0.1441+1.3755i\\[1 em]x_6 &= -0.1441-1.3755i \end{aligned} $$Explanation
Polynomial $ -x^6+x^3+4x^2+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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