The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.3177\\[1 em]x_2 &= -1.3412+1.1615i\\[1 em]x_3 &= -1.3412-1.1615i \end{aligned} $$Polynomial $ x^3+3x^2+4x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.