Find roots of polynomial $$ p(x) = x^5-x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.1673\\[1 em]x_2 &= 0.7649+0.3525i\\[1 em]x_3 &= 0.7649-0.3525i\\[1 em]x_4 &= -0.1812+1.084i\\[1 em]x_5 &= -0.1812-1.084i \end{aligned} $$Explanation
Polynomial $ x^5-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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