Find roots of polynomial $$ p(x) = 6x^7-2x^6+4x^5+2x^4+7x^3+6x^2+x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8074\\[1 em]x_2 &= 0.1463+0.6371i\\[1 em]x_3 &= 0.1463-0.6371i\\[1 em]x_4 &= -0.4471+0.8713i\\[1 em]x_5 &= -0.4471-0.8713i\\[1 em]x_6 &= 0.8712+0.8675i\\[1 em]x_7 &= 0.8712-0.8675i \end{aligned} $$Explanation
Polynomial $ 6x^7-2x^6+4x^5+2x^4+7x^3+6x^2+x+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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