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## Main Question or Discussion Point

Does the discriminant have any specific definition? I've come across two discriminant definitions that don't seem to be very relevant to each other, and I was wondering if there is any particular property that discriminants convey. In finding roots and using the quadratic equation, I've seen ## D = b^2 - 4ac## and for multivariable calculus,I've seen ## D = f_{xx}f_{yy} - (f_{xy})^2##. These two equations don't seem very similar, yet are called discriminants (to my knowledge). Is there any single definition for a discriminant in mathematics? Does it determine anything specific about functions? Are there more definitions for discriminants? I realize these are just terms for different operations but it seemed odd they have the same names.