definition
An expression that gives information about the roots of a polynomial; for example, the expression D = b2 - 4ac determines whether the roots of the quadratic equation ax2 + bx + c = 0 are real and distinct (D > 0), real and equal (D = 0) or complex (D < 0).
definition
The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in Pn-1 is singular.
definition
Serving to discriminate.
This implies the vanishing of the discriminant of the original form.
The expression (ab) 4 properly appertains to a quartic; for a quadratic it may also be written (ab) 2 (cd) 2, and would denote the square of the discriminant to a factor pres.
The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.
The way to get around the problem is to use a discriminant in the record declaration.
Conclusions The MDAS is a highly consistent and reliable measure which has good discriminant and concurrent validity.
By discriminant Chapter Index Here a type can be given a discriminant so that a whole family of types may be declared.
Approximation of a discriminant function or regression function using a hyperplane.
Structural, concurrent, and discriminant validity of the test scores were evaluated.
Discriminants.-The discriminant of a homogeneous polynomial in k variables is the resultant of the k polynomials formed by differentiations in regard to each of the variables.
For the quadratic it is the discriminant (ab) 2 and for ax2 the cubic the quadratic covariant (ab) 2 axbx.
This method of solution fails when the discriminant R vanishes, for then the Hessian has equal roots, as also the cubic f.
The discriminant, whose vanishing is the condition that f may possess two equal roots, has the expression j 2 - 6 i 3; it is nine times the discriminant of the cubic resolvent k 3 - 2 ik- 3j, and has also the expression 4(1, t') 6 .
The discriminant of the product of two forms is equal to the product of their discriminants multiplied by the square of their resultant.
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