Find roots of polynomial $$ p(x) = 6x^7-2x^6+4x^5+2x^4+12x^3+9x^2+x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.7832\\[1 em]x_2 &= 0.107+0.5155i\\[1 em]x_3 &= 0.107-0.5155i\\[1 em]x_4 &= -0.523+0.9717i\\[1 em]x_5 &= -0.523-0.9717i\\[1 em]x_6 &= 0.9743+0.9706i\\[1 em]x_7 &= 0.9743-0.9706i \end{aligned} $$Explanation
Polynomial $ 6x^7-2x^6+4x^5+2x^4+12x^3+9x^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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