I'm really stuck on this hard system of equations: a+b+c = 2, ab+bc+ac = -11, and abc = -12. can anyone show me how to solve this?asap!

Oh boy. I don't know how to solve this off the top of my head so this answer may ramble a bit as I figure it out as I go along.

At least two numbers have to be close in value, one positive and one negative, in order for a+b+c to be true

Let's see, ABC=-12

If one letter was 4, 1, and -3 they would add to 2 and multiply to -12. I got these by just trying a bunch of combinations.

I'm pretty sure these are the right numbers, but which is which we need the AB+BC+AC formula to figure out.

IF: a=4 b=1 c=-3
4 -3 -12 = -11. Wow, first try, for reals!

A equals 4. B=1. C=-3

Would other combinations work?
a=1 b=-3 c=4
-3 + -12 + 4 = -11

Yes, other combinations work as well. Well, you have your numbers and two ways they can go. Hope this helps!