Cubic congruences and binary quadratic forms

Let $p \gt 3$ be a prime, $a_1,a_2,a_3\in \mathbb Z$, and let $N_p(x^3+a_1x^2+a_2x+a_3)$ denote the number of solutions to the congruence $x^3+a_1x^2+a_2x+a_3\equiv 0\pmod p$. We give an explicit criterion for $N_p(x^3+a_1x^2+a_2x+a_3)=3$ via binary quadratic forms.