The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2267\\[1 em]x_2 &= 0.8152\\[1 em]x_3 &= 5.4115 \end{aligned} $$Polynomial $ x^3-6x^2+3x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.