Find roots of polynomial $$ p(x) = x^5-57x^4+1249x^3-13191x^2+67438x-134604 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 10.9011\\[1 em]x_2 &= 13.3544\\[1 em]x_3 &= 19.0788\\[1 em]x_4 &= 6.8328+1.3325i\\[1 em]x_5 &= 6.8328-1.3325i \end{aligned} $$Explanation
Polynomial $ x^5-57x^4+1249x^3-13191x^2+67438x-134604 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.
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