Find roots of polynomial $$ p(x) = 6x^7-2x^6+4x^5+2x^4+7x^3-6x^2+18x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.157\\[1 em]x_2 &= -0.9546+0.7622i\\[1 em]x_3 &= -0.9546-0.7622i\\[1 em]x_4 &= 0.2363+1.1896i\\[1 em]x_5 &= 0.2363-1.1896i\\[1 em]x_6 &= 0.9635+0.723i\\[1 em]x_7 &= 0.9635-0.723i \end{aligned} $$Explanation
Polynomial $ 6x^7-2x^6+4x^5+2x^4+7x^3-6x^2+18x+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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