The discriminant of a polynomial of degree is quasi-homogeneous of degree in the coefficients, if, for every , the coefficient of is given the weight . It is also quasi-homogeneous of the same degree, if, for every , the coefficient of is given the weight . This is a consequence of the general fact that every polynomial which is homogeneous and symmetric in the roots may be expressed as a quasi-homogeneous polynomial in the elementary symmetric functions of the roots.
The discriminant of a polynomial of degree is quasi-homogeneous of degree in the coefficients if for every  the coefficient of is given the weight  It is also quasi-homogeneous of the same degree if for every  the coefficient of is given the weight  This is a consequence of the general fact that every polynomial which is homogeneous and symmetric in the roots may be expressed as a quasi-homogeneous polynomial in the elementary symmetric functions of the roots