A discriminant is a polynomial expression in the coefficients that vanishes when the associated polynomial has a repeated root.
The quadratic discriminant is for . Over the real numbers, the equation has two, one, or no real roots according as is positive, zero, or negative.
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In mathematics, particularly in algebra, the discriminant is a specific quantity associated with a polynomial equation that provides information about the nature of its roots. The most common context in which the discriminant is discussed is in quadratic equations, which are polynomial equations of the form: \[ ax^2 + bx + c = 0 \] where \( a \), \( b \), and \( c \) are coefficients, and \( a \neq 0 \).