Discriminant Sentence Examples

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.