Find roots of polynomial $$ p(x) = x^6-x^3+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9397+0.342i\\[1 em]x_2 &= 0.9397-0.342i\\[1 em]x_3 &= -0.1737+0.9848i\\[1 em]x_4 &= -0.1737-0.9848i\\[1 em]x_5 &= -0.766+0.6428i\\[1 em]x_6 &= -0.766-0.6428i \end{aligned} $$Explanation
Polynomial $ x^6-x^3+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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