The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.0705\\[1 em]x_2 &= -1.5742\\[1 em]x_3 &= 2.2538 \end{aligned} $$Polynomial $ 4x^3-3x^2-14x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.