Find roots of polynomial $$ p(x) = 42x^6-72x^5+20x^4+8x^3+21x^2+18x+1 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.0596\\[1 em]x_2 &= -0.4886\\[1 em]x_3 &= -0.1197+0.6552i\\[1 em]x_4 &= -0.1197-0.6552i\\[1 em]x_5 &= 1.2509+0.5271i\\[1 em]x_6 &= 1.2509-0.5271i \end{aligned} $$Explanation
Polynomial $ 42x^6-72x^5+20x^4+8x^3+21x^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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