The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.2266\\[1 em]x_2 &= 2.52\\[1 em]x_3 &= 5.2534 \end{aligned} $$Polynomial $ x^3-8x^2+15x-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.