Find roots of polynomial $$ p(x) = x^7+x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.1608\\[1 em]x_2 &= 1.1303+0.5664i\\[1 em]x_3 &= 1.1303-0.5664i\\[1 em]x_4 &= -0.7765+0.8996i\\[1 em]x_5 &= -0.7765-0.8996i\\[1 em]x_6 &= 0.2266+1.2147i\\[1 em]x_7 &= 0.2266-1.2147i \end{aligned} $$Explanation
Polynomial $ x^7+x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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