1. Using alpha and D in place of 'a' and 'd' (which notation I've seen is pretty common), it seems from grade school algebraic manipulation that we have this as long as D > 0.

So in general,

.

Suppose D > 0. Set

then we can choose for example b = a, and we are done.

Suppose D < 0. Let's just make sure the above result holds with complex numbers. (I'm not sure this is necessary, but it doesn't hurt to check.)

. So we see there is no way to make this negative when D < 0.

2. Again write out from definitions and see if there is an answer just using algebra taught in grade school.

. Recall the norm for complex numbers,

which is just the distance from the origin to that point in the complex plane. So we see that

and

.

So when in doubt, go back to definitions and see if something relatively simple doesn't pop out.