Quadratic Trouble

Let $f(x) = ax^2 + bx + c$ , where $a,b,c$ are integers. Suppose that $f(1)=0, 50<f(7)<60, 70<f(8)<80$ and $500m<f(100)<500(m+1)$ for some integer $m$ .

Also, let the non-integer root of $f(x)$ be $n$ . Find $m+2n$ .