The following trinomial is in the form ax^2 + bx + c.
Find the two integers that have a product of ac and 
a sum of b. Do not factor the trinomials. 

15t^2 - 17t - 4

Here a = 15, b = -17, c = -4

ac = (15)(-4) = -60

You are to find two integers such that if you multiply 
them together you get -60, and if you add them you 
get -17.

So you write down all the pairs of integers that have 
product -60, and then check to see if their sum is -17:

+1 and -60, their product is -60 and their sum is -59
-1 and +60, their product is -60 and their sum is +59
+2 and -30, their product is -60 and their sum is -28
-2 and +30, their product is -60 and their sum is +28 
+3 and -20, their product is -60 and their sum is -17
-3 and +20, their product is -60 and their sum is +17
+4 and -15, their product is -60 and their sum is -11
-4 and +15, their product is -60 and their sum is +11 
+5 and -12, their product is -60 and their sum is -7
-5 and +12, their product is -60 and their sum is +7
+6 and -10, their product is -60 and their sum is -4
-6 and +10, their product is -60 but their sum is +4 

It's the case colored red above, +3 and -20. I could
have quit when I got to that pair of integers, but I 
thought I'd go ahead and list them all so you could 
see how to.

Edwin