SAT Right triangles Question

The function $f$ is defined by $f(x)=a{x}^2+bx+c$ , where $a,b$ , and $c$ are constants. The graph of $y=f(x)$ in the $xy$ -plane passes through the points (10, 0) and (-5, 0). If $a$ is an integer greater than 1, which of the following could be the value of $a+b$ ?