Find roots of polynomial $$ p(x) = 4x^6+2x^5+x^4+x^3+9x^2+9x+7 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.3858+0.8543i\\[1 em]x_2 &= -0.3858-0.8543i\\[1 em]x_3 &= -0.8454+0.6362i\\[1 em]x_4 &= -0.8454-0.6362i\\[1 em]x_5 &= 0.9812+0.9037i\\[1 em]x_6 &= 0.9812-0.9037i \end{aligned} $$Explanation
Polynomial $ 4x^6+2x^5+x^4+x^3+9x^2+9x+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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