Find roots of polynomial $$ p(x) = x^6+64 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.7321+i\\[1 em]x_2 &= 1.7321-i\\[1 em]x_3 &= -1.7321+i\\[1 em]x_4 &= -1.7321-i\\[1 em]x_5 &= 2i\\[1 em]x_6 &= -2i \end{aligned} $$Explanation
Polynomial $ x^6+64 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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