Number of Roots of a Quadratic

Let $f$ be the quadratic function with leading coefficient $1$ whose graph is tangent to that of the lines $y=-5x+6$ and $y=x-1$. The sum of the coefficients of $f$ is $\tfrac pq$, where $p$ and $q$ are positive relatively prime integers. Find $100p + q$.

(SOURCE: NIMO 24)