$\displaystyle y=\frac{-x^2+ax}{x-2b}$, find the range of values of $\displaystyle b$ for which the graph of $\displaystyle y=f(x)$ has two turning points.

I am able to solve it by finding dy/dx and make sure that dy/dx has roots.

My question is this,

Is there any other way to solve this without using differentiation?

Please enlighten me...thank you!