Find roots of polynomial $$ p(x) = 6x^7-2x^6+4x^5+2x^4-1000000x^3+9x^2+x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.0145\\[1 em]x_2 &= -20.1144\\[1 em]x_3 &= 20.2805\\[1 em]x_4 &= -0.0072+0.0125i\\[1 em]x_5 &= -0.0072-0.0125i\\[1 em]x_6 &= 0.0836+20.2129i\\[1 em]x_7 &= 0.0836-20.2129i \end{aligned} $$Explanation
Polynomial $ 6x^7-2x^6+4x^5+2x^4-1000000x^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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