In the solution of this problem, why choose the positive square root?

I was solving the following problem:

I made it but I got confused by something: I’ve obtained more solutions than I should. I went to see the solution in hope of clearing it up, the solution is:

Now here is where I got confused:

QUESTION: They assumed that $q_1 + q_2 geq 0$, was that made out of mathematical convenience or choosing $q_1 + q_2 geq 0$ has some physical meaning? It’s not clear to me why choose the positive square root here.