Find roots of polynomial $$ p(x) = 8x^6-9x^5+2x^4-100x^3+24x^2-12x+6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.3636\\[1 em]x_2 &= 2.6612\\[1 em]x_3 &= -0.0621+0.4039i\\[1 em]x_4 &= -0.0621-0.4039i\\[1 em]x_5 &= -0.8878+1.9629i\\[1 em]x_6 &= -0.8878-1.9629i \end{aligned} $$Explanation
Polynomial $ 8x^6-9x^5+2x^4-100x^3+24x^2-12x+6 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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