Generalization of the multiplicity to real (http://planetmath.org/RealFunction) and complex functions (by rspuzio): If the function is continuous on some open set and for some , then the zero of at is said to be of multiplicity if is continuous in but is not.
If , we speak of a multiple zero; if , we speak of a simple zero. If , then actually the number is not a zero of , i.e. .
Some properties (from which 2, 3 and 4 concern only polynomials):
The zero of a polynomial with multiplicity is a zero of the with multiplicity .
The zeros of the polynomial are same as the multiple zeros of .
The quotient has the same zeros as but they all are .
The zeros of any irreducible polynomial are .
|Date of creation||2013-03-22 14:24:18|
|Last modified on||2013-03-22 14:24:18|
|Last modified by||pahio (2872)|
|Synonym||order of the zero|
|Defines||zero of order|