Find roots of polynomial $$ p(x) = x^8+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.3827+0.9239i\\[1 em]x_2 &= 0.3827-0.9239i\\[1 em]x_3 &= -0.3827+0.9239i\\[1 em]x_4 &= -0.3827-0.9239i\\[1 em]x_5 &= -0.9239+0.3827i\\[1 em]x_6 &= -0.9239-0.3827i\\[1 em]x_7 &= 0.9239+0.3827i\\[1 em]x_8 &= 0.9239-0.3827i \end{aligned} $$Explanation
Polynomial $ x^8+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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