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Binary Quadratic Form Discriminant


The discriminant of a binary quadratic form

 au^2+buv+cv^2

is defined by

 d=4ac-b^2.

It is equal to four times the corresponding binary quadratic form determinant.

Unfortunately, some authors define the discriminant of a binary quadratic form as the negative of d above, so care is needed when consulting the literature.


See also

Binary Quadratic Form, Binary Quadratic Form Determinant, Class Number, Positive Definite Quadratic Form, Positive Semidefinite Quadratic Form

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Cite this as:

Weisstein, Eric W. "Binary Quadratic Form Discriminant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BinaryQuadraticFormDiscriminant.html

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