Find roots of polynomial $$ p(x) = 42x^6-12x^5+20x^4+8x^3-18x^2+18x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.0527\\[1 em]x_2 &= -0.8548\\[1 em]x_3 &= 0.5932+0.4527i\\[1 em]x_4 &= 0.5932-0.4527i\\[1 em]x_5 &= 0.0035+0.9742i\\[1 em]x_6 &= 0.0035-0.9742i \end{aligned} $$Explanation
Polynomial $ 42x^6-12x^5+20x^4+8x^3-18x^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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