Find roots of polynomial $$ p(x) = x^6-3x^5+3x^4-x^3-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.618\\[1 em]x_2 &= 1.618\\[1 em]x_3 &= -0.0707+0.7587i\\[1 em]x_4 &= -0.0707-0.7587i\\[1 em]x_5 &= 1.0707+0.7587i\\[1 em]x_6 &= 1.0707-0.7587i \end{aligned} $$Explanation
Polynomial $ x^6-3x^5+3x^4-x^3-1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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