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 linear factors
( x - 2) ( x -7) m = 9
(x + 2) (x + 7) m = -9
(x - 1) ( x -14) m = 15
(x + 1) ( x + 14) m = -15