<P> In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset . For example, the number of times a given polynomial equation has a root at a given point . </P> <P> The notion of multiplicity is important to be able to count correctly without specifying exceptions (for example, double roots counted twice). Hence the expression, "counted with multiplicity". </P> <P> If multiplicity is ignored, this may be emphasized by counting the number of distinct elements, as in "the number of distinct roots". However, whenever a set (as opposed to multiset) is formed, multiplicity is automatically ignored, without requiring use of the term "distinct". </P>

Why is it important to consider multiplicity when determining the roots of a polynomial equation