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?
x2 – mx + 24 = 10
x2 – mx + 14 = 0
the coefficient of x is the sum of the factors of 14
the integer factors of +14 are (+2, +7) and (–2, –7)
and (+1, +14) and (–1, –14)
So m could equal +9 or –9 or +15 or –15
Therefore, m could have 4 possible values
.
+617 
