The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.6956\\[1 em]x_2 &= 1.3478+1.0289i\\[1 em]x_3 &= 1.3478-1.0289i \end{aligned} $$Polynomial $ x^3-2x^2+x+2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.