Find roots of polynomial $$ p(x) = 5x^5-36x^4+62x^3-46x^2+57x-6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.1143\\[1 em]x_2 &= 2.0288\\[1 em]x_3 &= 4.9979\\[1 em]x_4 &= 0.0295+1.0172i\\[1 em]x_5 &= 0.0295-1.0172i \end{aligned} $$Explanation
Polynomial $ 5x^5-36x^4+62x^3-46x^2+57x-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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