Find roots of polynomial $$ p(x) = x^8+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.0987+0.4551i\\[1 em]x_2 &= 1.0987-0.4551i\\[1 em]x_3 &= -0.4551+1.0987i\\[1 em]x_4 &= -0.4551-1.0987i\\[1 em]x_5 &= -1.0987+0.4551i\\[1 em]x_6 &= -1.0987-0.4551i\\[1 em]x_7 &= 0.4551+1.0987i\\[1 em]x_8 &= 0.4551-1.0987i \end{aligned} $$Explanation
Polynomial $ x^8+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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