The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2696\\[1 em]x_2 &= -0.8376\\[1 em]x_3 &= 1.1072 \end{aligned} $$Polynomial $ -4x^3+4x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.