# Discriminant

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Related to Discriminant: discriminant function

## discriminant

[di′skrim·ə·nənt]
(mathematics)
The quantity b 2- 4 ac, where a,b,c are coefficients of a given quadratic polynomial: ax 2+ bx + c.
More generally, for the polynomial equation a0 xn + a1 xn -1+···+ anx0= 0, a02 n-2times the product of the squares of all the differences of the roots of the equation, taken in pairs.

## Discriminant

The discriminant of a polynomial

P(x) = a0xn + a1xn−1 + … + an

is the expression in which the product is distributed over all possible differences of the roots α1, β2, … , αn of the equation P (x) = 0. The discriminant vanishes if and only if there are equal roots among the roots of the polynomial. The discriminant can be expressed through the coefficients of the polynomial P(x) by representing it in the form of a determinant consisting of these coefficients. Thus, for the second-degree polynomial ax2 + bx + c, the discriminant is b2 − 4ac. For x3 + px + q, the discriminant is −4p3 −27q2. The discriminant differs only by a factor a0 from the resultant R(P, P′) of the polynomial P(x) and its derivative P′(x).

References in periodicals archive ?
Discriminant functions are especially effective in the case of gulls (Laridae), allowing correct sexing from 90 to 100 % of individuals from different species (Mawhinney & Diamond 1999, Chochi et al.
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To ensure the validity and reliability of the measurement model, convergence validity and discriminant validity were examined.
For this purpose, the standard Discriminant Function Analysis module STATISTICA, intended for statistical analysis and data processing, was originally used.
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2] - 4x + 5 is solved using the quadratic formula, the discriminant is -4.
Enders (2003) suggested that linear discriminant function analysis is a desirable analysis for evaluating multivariate group differences.
Discriminant function analysis described by Dabholkar (1992) was used to construct the selection indices involving six characters, seed yield per plant ([X.
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2] test for multivariate analysis and discriminant function analysis with SPSS.
Finally, we use frequentist linear discriminant analysis to predict the age classes of harvested deer from their eye lens dry mass.
The discriminant validity of the inventory, assessed with a sample of 200 doctors, revealed that it discriminated well between doctors with moderate to severe burnout and doctors with normal to mild burnout (pless than 0.

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