The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 3.1324\\[1 em]x_2 &= 0.8446+0.6036i\\[1 em]x_3 &= 0.8446-0.6036i\\[1 em]x_4 &= -0.4108+0.651i\\[1 em]x_5 &= -0.4108-0.651i \end{aligned} $$Polynomial $ x^5-4x^4+3x^3-x^2+x-2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.