Find roots of polynomial $$ p(x) = 42x^6-12x^5+20x^4+8x^3+30000x^2+18x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.0003+0.0058i\\[1 em]x_2 &= -0.0003-0.0058i\\[1 em]x_3 &= -3.5687+3.6684i\\[1 em]x_4 &= -3.5687-3.6684i\\[1 em]x_5 &= 3.7119+3.6732i\\[1 em]x_6 &= 3.7119-3.6732i \end{aligned} $$Explanation
Polynomial $ 42x^6-12x^5+20x^4+8x^3+30000x^2+18x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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