+501 Find the product of all positive integer values of $c$ such that $8x^2+15x+c=0$ has two real roots.
+1224 The discriminant needs to be greater than 0.
\(\Delta = b^2- 4ac = 225 - 32c > 0\)
\(c < \frac{225}{32}\)
225/32 is equal to 7.03125, so c can be any integer from 1 to 7. The sum is 28.
