Find roots of polynomial $$ p(x) = x^6-82x^5+4x^4+82x^3-125x^2-74x+120 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.792\\[1 em]x_2 &= 81.9392\\[1 em]x_3 &= 0.7199+0.9511i\\[1 em]x_4 &= 0.7199-0.9511i\\[1 em]x_5 &= -1.0854+0.3487i\\[1 em]x_6 &= -1.0854-0.3487i \end{aligned} $$Explanation
Polynomial $ x^6-82x^5+4x^4+82x^3-125x^2-74x+120 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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