Find roots of polynomial $$ p(x) = x^7+2x^6+x^5+2x^4+2x^3-3x^2-3x+7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.7981\\[1 em]x_2 &= 0.8277+0.4479i\\[1 em]x_3 &= 0.8277-0.4479i\\[1 em]x_4 &= -1.2109+0.7953i\\[1 em]x_5 &= -1.2109-0.7953i\\[1 em]x_6 &= 0.2823+1.4194i\\[1 em]x_7 &= 0.2823-1.4194i \end{aligned} $$Explanation
Polynomial $ x^7+2x^6+x^5+2x^4+2x^3-3x^2-3x+7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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