Given that the polynomial x^2 - 15x + t = 0 has only positive integer roots, find the average of all distinct possible values of t.
+2668 The roots of the quadratic are \({15 \pm \sqrt{225-4t} \over 2}\)
Note that \(\sqrt {225 - 4t}\) must be an odd, positive integer.
To solve, set \(\sqrt{225 - 4t}\) equal to 13, 11, 9, 7, 5, 3, and 1.
Now, solve for t in all cases and find the average.
