Find roots of polynomial $$ p(x) = 6x^7+2x^6+4x^5+2x^4+7x^3+9x^2+4x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8898\\[1 em]x_2 &= -0.0439+0.7134i\\[1 em]x_3 &= -0.0439-0.7134i\\[1 em]x_4 &= -0.5157+0.9068i\\[1 em]x_5 &= -0.5157-0.9068i\\[1 em]x_6 &= 0.8378+0.8036i\\[1 em]x_7 &= 0.8378-0.8036i \end{aligned} $$Explanation
Polynomial $ 6x^7+2x^6+4x^5+2x^4+7x^3+9x^2+4x+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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