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?
x^2-mx+24 = 10
subtract 10 from both sides x2 – mx + 14 = 0
integers that multiply to 14 (+7)(+2)
(–7)(–2)
(+1)(+14)
(–1)(–14)
possible values of m –9
+9
–15
+15
total number of
possible values of m 4
.
+1839 
