How does the DISCRIMINANT really work?
I have the following equation (depended on param a)
I want to find out what the behavior of this equation after changing the value (by behavior I mean finding out how will the root count change when I put x or y instead of a). So for that purpose I thought it might be useful to find the D. If i'm not wrong when we have , then we can simply use this formula:
so after having this done, I thought maybe I can find out where my equation has only 1 root:
but after putting for example , I quickly noticed that there my equation has no roots(real roots I think).
Can someone explain me what I've missed here? Shouldn't , work just fine (I mean give me only 1 root)?