Find roots of polynomial $$ p(x) = 6x^7-2x^6+4x^5+2x^4+7x^3+5x^2+5x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.5976\\[1 em]x_2 &= 0.0729+0.8468i\\[1 em]x_3 &= 0.0729-0.8468i\\[1 em]x_4 &= -0.5212+0.6941i\\[1 em]x_5 &= -0.5212-0.6941i\\[1 em]x_6 &= 0.9137+0.8382i\\[1 em]x_7 &= 0.9137-0.8382i \end{aligned} $$Explanation
Polynomial $ 6x^7-2x^6+4x^5+2x^4+7x^3+5x^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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