Find roots of polynomial $$ p(x) = x^7+7x^6-6x^4+2x+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -6.8729\\[1 em]x_2 &= 0.9428+0.4i\\[1 em]x_3 &= 0.9428-0.4i\\[1 em]x_4 &= -0.0465+0.8313i\\[1 em]x_5 &= -0.0465-0.8313i\\[1 em]x_6 &= -0.9598+0.282i\\[1 em]x_7 &= -0.9598-0.282i \end{aligned} $$Explanation
Polynomial $ x^7+7x^6-6x^4+2x+5 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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