Find roots of polynomial $$ p(x) = 6x^7+2x^6+5x^5+2x^4+7x^3+6x^2+5x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6496\\[1 em]x_2 &= -0.07+0.8277i\\[1 em]x_3 &= -0.07-0.8277i\\[1 em]x_4 &= -0.5517+0.782i\\[1 em]x_5 &= -0.5517-0.782i\\[1 em]x_6 &= 0.7799+0.7809i\\[1 em]x_7 &= 0.7799-0.7809i \end{aligned} $$Explanation
Polynomial $ 6x^7+2x^6+5x^5+2x^4+7x^3+6x^2+5x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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