The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?
Simplify as
x^2 - mx + 14 = 0
Possible factorizations
(x - 2) (x -7) = 0 m = -9
(x + 2) (x + 7) = 0 m = 9
(x -14) (x -1) = 0 m = -15
(x + 14) ( x + 1) = 0 m = 15
+1678 
