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discriminants

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Plural form of discriminant.
A distinguishing feature or characteristic.

Discriminants might refer to
In algebra, the Discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them. For example, the discriminant of the quadratic polynomial* * * * a * * x * * 2 * * * + * b * x * + * c * * * {\displaystyle ax^{2}+bx+c} * * is * * * * * * b * * 2 * * * − * 4 * a * c * , * * * {\displaystyle b^{2}-4ac,} * * which is zero if and only if the polynomial has a double root, and (in the case of real coefficients) is positive if and only if the polynomial has two real roots. * More generally, for a polynomial of an arbitrary degree, the discriminant is zero if and only if it has a multiple root, and, in the case of real coefficients, it is positive if and only if the number of non-real roots is a multiple of 4 when the degree is 4 or higher. * The discriminant is widely used in number theory, either directly or through its generalization as the discriminant of a number field. For factoring a polynomial with integer coefficients, the standard method consists in first factoring its reduction modulo, a prime number not dividing the discriminant (and not dividing the leading coefficient). In algebraic geometry, the discriminant with respect to one of the variables characterizes the points of a hypersurface where the implicit function theorem does not apply. * The term "discriminant" was coined in 1851 by the British mathematician James Joseph Sylvester. * *

Discriminants might refer to

In algebra, the Discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them. For example, the discriminant of the quadratic polynomial*
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* which is zero if and only if the polynomial has a double root, and (in the case of real coefficients) is positive if and only if the polynomial has two real roots.
* More generally, for a polynomial of an arbitrary degree, the discriminant is zero if and only if it has a multiple root, and, in the case of real coefficients, it is positive if and only if the number of non-real roots is a multiple of 4 when the degree is 4 or higher.
* The discriminant is widely used in number theory, either directly or through its generalization as the discriminant of a number field. For factoring a polynomial with integer coefficients, the standard method consists in first factoring its reduction modulo, a prime number not dividing the discriminant (and not dividing the leading coefficient). In algebraic geometry, the discriminant with respect to one of the variables characterizes the points of a hypersurface where the implicit function theorem does not apply.
* The term "discriminant" was coined in 1851 by the British mathematician James Joseph Sylvester.
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