Find roots of polynomial $$ p(x) = x^5-x^4-x^3-x^2-x-1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.966\\[1 em]x_2 &= 0.1954+0.8489i\\[1 em]x_3 &= 0.1954-0.8489i\\[1 em]x_4 &= -0.6784+0.4585i\\[1 em]x_5 &= -0.6784-0.4585i \end{aligned} $$Explanation
Polynomial $ x^5-x^4-x^3-x^2-x-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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