smc

If the roots of the quadratic $A{x}^2+Bx+C=0$ are equal, then $B^2-4AC=0$. Plugging in $A=1,B=-p,C=p$ into the equation gives $p^2-4p=0$. This leads to $p=0,4$, so there are two values of $p$ that work, giving answer $\boxed{2}$.