You indeed need to calculate the discriminant.
What this question means is actually, how many intersections are there with the x-axis.
You probably are familiar with the fact that if D > 0 there are two intersections, if D = 0, there is one, and if D < 0 there are none. That is it for the number of roots, for the type, I have no idea what they mean either.
(It occurred to me that you might actually not know what they mean with the discriminant, if you don't, please post that and I'll try to help you further.)