Given that the polynomial x^2 - 15x + t = 0 has only positive integer roots, find the average of all distinct possible values of t.
+129850 x^2 - 15x + t = 0
Note that we have these possibilities for t
(x - 14) ( x - 1) t = 14
(x - 13) ( x - 2) t = 26
(x - 12) ( x - 3) t = 36
(x - 11) ( x - 4) t = 44
(x - 10) (x - 5) t = 50
(x - 9) ( x - 6) t = 54
(x - 8) ( x - 7) t = 56
Avg = ( 14 + 26 + 36 + 44 + 50 + 54 + 56) / 7 = 280 / 7 = 40
