Find roots of polynomial $$ p(x) = 6x^7+2x^6+4x^5+2x^4+7x^3+6x^2+5x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6618\\[1 em]x_2 &= -0.0505+0.8074i\\[1 em]x_3 &= -0.0505-0.8074i\\[1 em]x_4 &= -0.5905+0.7556i\\[1 em]x_5 &= -0.5905-0.7556i\\[1 em]x_6 &= 0.8052+0.7791i\\[1 em]x_7 &= 0.8052-0.7791i \end{aligned} $$Explanation
Polynomial $ 6x^7+2x^6+4x^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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