$$4p^3+2p^2+19p-5 = 0$$
Answer
$$ \begin{matrix}p_1 = 0.25301 & p_2 = -0.3765+2.19061i & p_3 = -0.3765-2.19061i \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Polynomial Equations Solver