Find roots of polynomial $$ p(x) = y^6+1 $$
Answer
The roots of polynomial $ p(y) $ are:
$$ \begin{aligned}y_1 &= 0.866+0.5i\\[1 em]y_2 &= 0.866-0.5i\\[1 em]y_3 &= -0.866+0.5i\\[1 em]y_4 &= -0.866-0.5i\\[1 em]y_5 &= i\\[1 em]y_6 &= -i \end{aligned} $$Explanation
Polynomial $ y^6+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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