Quartic Definition

Quartic Sentence Examples

• 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 quartic has four equal roots, that is to say, is a perfect fourth power, when the Hessian vanishes identically; and conversely.

• The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.

• The simplest form to which the quartic is in general reducible is +6mxix2+x2, involving one parameter m; then Ox = 2m (xi +x2) +2 (1-3m2) x2 ix2; i = 2 (t +3m2); j= '6m (1 - m) 2; t= (1 - 9m 2) (xi - x2) (x21 + x2) x i x 2.

• It is on a consideration of these factors of t that Cayley bases his solution of the quartic equation.