discriminant
Speech parts
1. discriminant - Noun
2. discriminant - Adjective
Meaning
The eliminant of the n partial differentials of any homogenous function of n variables. See Eliminant.
Source: Webster's dictionarySynonyms
Antonyms
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Examples
Algebraically, this involves calculating the discriminant : The curve is non-singular if and only if the discriminant is not equal to zero.
As the discriminant is a symmetric function in the roots, it can also be expressed in terms of the coefficients of the polynomial, since the coefficients are the elementary symmetric polynomials in the roots; such a formula is given below.
Definition In terms of the roots, the discriminant is given by : where is the leading coefficient and are the roots (counting multiplicity ) of the polynomial in some splitting field.
A second form of cancellation can occur between the terms b 2 and 4ac of the discriminant, which can lead to loss of up to half of correct significant figures.
As shown in Figure 3, if the discriminant is positive, the graph touches the x -axis at two points; if zero, the graph touches at one point; and if negative, the graph does not touch the x -axis.
For example, in the graphs shown in figure to the right, the discriminant in the first case is 64, and in the second case is −368.