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Related to Discriminant: discriminant function


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.



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 analysis is used to serve the objective of the study.
Income-based models scored in reliability, discriminant and predicative validity, but largely fell short in convergent and nomological validity, while the capitalized cost-approach lacked reliability and predicative validity.
We conducted a canonical discriminant function analysis to test whether songs could be correctly assigned to the birds that produced them.
Keywords: bankruptcy, discriminant analysis, data envelopment analysis, credit scoring
The resulting sample was then subjected to a two-group step-wise discriminant analysis, utilizing Wilks' Lambda and an unbiased classification procedure to test the model's statistical and classification efficacy.
A discriminant analysis was conducted in order to establish factors of difference among the students from the various faculties.
In the third phase, a discriminant function analysis was performed on the consensus groupings using the items of the IMI to form meaningful scales of items that separated the groupings (BE neighbourhoods).
The statistical model that satisfies these requirements is discriminant analysis.
Assumptions for the main analysis were also tested, including linearity, multivariate normality, homogeneity of variance and covariance matrices for discriminant function analysis (Box's M), homogeneity of variance for the univariate situation (Levene's Test), and singularity and multicollinearity.
Linear discriminant analysis (LDA) [2] preserves discriminative information between data of different classes and finds the optimal set of projection vectors by maximizing the ratio between the interclass and intraclass scatters.
Discriminant analyses were then conducted to differentiate and characterize the soil with the goal of developing and testing the method for soil class determination based on either its spectral data or analytical characteristics.