Find roots of polynomial $$ p(x) = x^7+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.3459\\[1 em]x_2 &= 1.2126+0.584i\\[1 em]x_3 &= 1.2126-0.584i\\[1 em]x_4 &= -0.8392+1.0523i\\[1 em]x_5 &= -0.8392-1.0523i\\[1 em]x_6 &= 0.2995+1.3122i\\[1 em]x_7 &= 0.2995-1.3122i \end{aligned} $$Explanation
Polynomial $ x^7+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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