The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 4.2133\\[1 em]x_2 &= -0.1067+1.3738i\\[1 em]x_3 &= -0.1067-1.3738i \end{aligned} $$Polynomial $ x^3-4x^2+x-8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.