Find roots of polynomial $$ p(x) = x^8-4x^7+6x^6-4x^5+x^4-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.618\\[1 em]x_2 &= 1.618\\[1 em]x_3 &= -0.3002+0.6248i\\[1 em]x_4 &= -0.3002-0.6248i\\[1 em]x_5 &= 0.5+0.866i\\[1 em]x_6 &= 0.5-0.866i\\[1 em]x_7 &= 1.3002+0.6248i\\[1 em]x_8 &= 1.3002-0.6248i \end{aligned} $$Explanation
Polynomial $ x^8-4x^7+6x^6-4x^5+x^4-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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