Find roots of polynomial $$ p(x) = x^6+x^5+x^4+x^3+7x^2+5x+2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.3754+0.4122i\\[1 em]x_2 &= -0.3754-0.4122i\\[1 em]x_3 &= -1.1332+1.1282i\\[1 em]x_4 &= -1.1332-1.1282i\\[1 em]x_5 &= 1.0085+1.2245i\\[1 em]x_6 &= 1.0085-1.2245i \end{aligned} $$Explanation
Polynomial $ x^6+x^5+x^4+x^3+7x^2+5x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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