Find roots of polynomial $$ p(x) = x^5+x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7549\\[1 em]x_2 &= 0.8774+0.7449i\\[1 em]x_3 &= 0.8774-0.7449i\\[1 em]x_4 &= -0.5+0.866i\\[1 em]x_5 &= -0.5-0.866i \end{aligned} $$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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