An expression which is a symmetric polynomial is the discriminant of a polynomial with real or complex coefficients .
In algebra , the discriminant of a polynomial with real or complex coefficients is a certain expression in the coefficients of the polynomial which is a symmetric polynomial in the coefficients and gives information on the nature of the roots ; in particular , it is equal to zero if and only if the polynomial has a multiple root ( i.e . a root with multiplicity greater than one ) in the complex numbers .
Discriminant