Studying for gmat. Most equations with a number larger than 1 at the start are out of my league but I'll give it a shot. I had to do some searching on factoring this way but I need the practice. I don't see many of that type if at all on the test...
First, refer to this article
https://www.mathsisfun.com/algebra/factoring-quadratics.html
I'll edit my post to show my work but it is good to read before I finish.
2x² + 7x - 15 = 0
1) Multiply 2 and -15 = -30
2) Sum of 7
--- Find set of numbers that multiply to -30 and add to 7
3) 10 and -3
4) Plug in for 7x.
5) 2x² + 10x - 3x - 15
6) Factor: 2x (x + 5) - 3 (x + 5)
7) Common factor is x + 5
8) Group -> (2x-3)(x+5)
9) Roots are 3/2 and -5
10) R > S thus 3/2 = R and -5 = S
11) R - S = 3/2 - (-5) = 3/2 + 10/2 = 13/2
Do we have an answer key for the second question?? I'm getting b = -4
PS: Thanks for the question it cleared up some things about factoring quadratics
Easy once you know the trick