The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.8847\\[1 em]x_2 &= 0.4423+0.2949i\\[1 em]x_3 &= 0.4423-0.2949i \end{aligned} $$Polynomial $ 4x^3-2x+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.