Find roots of polynomial $$ p(x) = x^5-5x^4+4x^3-3x^2+5x-6 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 4.1629\\[1 em]x_2 &= 0.9275+0.6278i\\[1 em]x_3 &= 0.9275-0.6278i\\[1 em]x_4 &= -0.5089+0.9435i\\[1 em]x_5 &= -0.5089-0.9435i \end{aligned} $$Explanation
Polynomial $ x^5-5x^4+4x^3-3x^2+5x-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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