I feel dumb asking this question. I know the roots should be positive 3 and positive 5. But when I use the equation I get a negative. I have never used the quadratic formula before so I dont understand if I am missing something basic.
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You are. The quadratic formula tells you the value(s) of x such that the quadratic equals zero. In your case you’ve correctly found that x = -3 and -5 are the values of x for which x^2 + 8x + 15 = 0.
That is not what the question is asking though. It is saying if we write
x^2 + 8x + 15 = (x + a)(x + b)
what is a + b? The intention was for people to factorise.
You can use the quadratic formula if you want though. We know that if x = -3,
(x + a)(x + b) = 0
If I put x = -3 above, we get
(a - 3)(b - 3) = 0
which means that a = 3 or b = 3. Try the same with x = -5 and you’ll see that the other value must be 5.
The expression when factorised BTW is (x + 3)(x + 5). Notice that when x = -3 and -5, the expression is zero, as expected.
Thank you so much I did not realize the quadratic formula is for when the expression is set to equal 0. That makes complete sense.