Find roots of polynomial $$ p(x) = x^6+2x^5+7x^4+7x^3+9x^2-x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2268+0.5789i\\[1 em]x_2 &= 0.2268-0.5789i\\[1 em]x_3 &= -0.9624+1.2157i\\[1 em]x_4 &= -0.9624-1.2157i\\[1 em]x_5 &= -0.2644+2.0578i\\[1 em]x_6 &= -0.2644-2.0578i \end{aligned} $$Explanation
Polynomial $ x^6+2x^5+7x^4+7x^3+9x^2-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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