First, we gotta set and , now set
The discriminant of this must be zero (such that and intersect in a single point), so
LetFind the set for "m" so that the graphs of y = mx and y = (x^2)+m intersect in a single point.
This must have only one solution, so the discriminant must be 0:
So either m = 0 or m = 4.
The following formula solves this equation
The expression it's called discriminant, which says who rules here!
If , then the equation has two real and different roots.
If , the the equation has two real and equal roots
If , the equation has two complex roots.
Hope it helps