It's easy to motivate using a picture. If you draw the parabola x^2 + bx + c then the minimum is at x = -b/2 and you can visually see that the average of the x-

It's easy to motivate using a picture. If you draw the parabola x^2 + bx + c then the minimum is at x = -b/2 and you can visually see that the average of the x-values of the roots is that minimum x = -b/2. So then u is simply the x-distance from the minimum to the roots. The more problematic step is the assumption that you can write the parabola as (x - r1)(x - r2). It isn't obvious why that is possible.