[Fyron]

Oh, you mean it returns an intercept that is zero relative to the target.

No, I don't mean that. I mean every quadratic function has 2 zeros/roots/x-intercepts. They are only a function of where the graph of the quadratic equation in question crosses the x axis. There will usually be two such locations, due to quadratic polynomial equations being parabolas and all (a parabola that has its vertex on the x axis will have both root solutions equal to each other).

The concept of zeros/roots/x-intercepts is unrelated to the problem of calculating where two ships should intercept each other in space. There is a lot of overlapping terminology, which is probably the root (hehehe) of the confusion. The zeros/roots/x-intercepts of the particular function we derived happen to be the time values (T) when the two objects will be in the same location at once, which is why they are useful for the solution.