# Only $$1$$ Intersects

Algebra Level pending

$$m$$ is an integer such that only one of the following three parabolas intersects the $$x$$-axis: \begin{align} y &= x^2-2mx+36, \\ y &= x^2-2mx-6m+16, \\ y &= x^2-2(m-1)x+2m^2-16m+49. \end{align} If $$a$$ and $$b$$ are the minimum and maximum values of $$m,$$ respectively, what is $$b-a?$$

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