Find roots of polynomial $$ p(x) = x^7-x^4+8 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.2719\\[1 em]x_2 &= 1.2591+0.5185i\\[1 em]x_3 &= 1.2591-0.5185i\\[1 em]x_4 &= -0.8559+1.1334i\\[1 em]x_5 &= -0.8559-1.1334i\\[1 em]x_6 &= 0.2327+1.2757i\\[1 em]x_7 &= 0.2327-1.2757i \end{aligned} $$Explanation
Polynomial $ x^7-x^4+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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