Find roots of polynomial $$ p(x) = 6x^7+10x^6+4x^5+2x^4+7x^3+9x^2+4x+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.3031\\[1 em]x_2 &= -0.0513+0.6573i\\[1 em]x_3 &= -0.0513-0.6573i\\[1 em]x_4 &= -0.85+0.6768i\\[1 em]x_5 &= -0.85-0.6768i\\[1 em]x_6 &= 0.7195+0.6923i\\[1 em]x_7 &= 0.7195-0.6923i \end{aligned} $$Explanation
Polynomial $ 6x^7+10x^6+4x^5+2x^4+7x^3+9x^2+4x+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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