The quadratic formula contains the discriminant formula inside a square root, with a +/- on the outside of it. If the discriminant is negative, the square root has no real values, so you can’t find a point where the quadratic crosses the x axis (since that’s what a solution to a quadratic means, a point where y=0). If it’s positive, you have 2 solutions, 1 for the + part of the +/- and 1 for the -. If it’s 0, then -0 is the same as +0 so there ends up only being 1 solution.
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