smc

From the quadratic equation, the two roots of the equation are $\frac{-p\pm \sqrt{p^2-4q}}{2}$. The positive difference between these roots is $\sqrt{p^2-4q}$. Setting $\sqrt{p^2-4q}=1$ and isolating $p$ gives $\sqrt{4q+1}$, or choice $\boxed{\sqrt{4q+1}}$.