Discriminant

In mathematics, a polynomial P(T) has a discriminant, which is a polynomial function of its coefficients, and discriminates the case of a multiple root (for which the graph of P(x) would touch the x-axis). This generalises to polynomials of any degree the case of a quadratic polynomial ax2 + bx + c, for which the discriminant is b2 − 4ac, the quantity under the square root sign in the formula for the roots (or quadratic formula). Discriminants in algebraic number theory are closely related, and contain information about ramification. In fact the more geometric types of ramification are also related to more abstract types of discriminant, making this a central algebraic idea in many applications.

Related Topics:
Mathematics - Polynomial - Coefficient - Quadratic polynomial - Square root - Formula for the roots - Algebraic number theory - Ramification

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