zero rule of product

For real and complex numbersMathworldPlanetmathPlanetmath, and more generally for elements of an integral domainMathworldPlanetmath, a product equals to zero if and only if at least one of the equals to zero.  For two elements a and b, we have

ab= 0a= 0b= 0.

For example, this rule can be used in solving polynomial equations:

x3-x2-2x+2= 0
(x3-x2)+(-2x+2)= 0
x2(x-1)-2(x-1)= 0
(x-1)(x2-2)= 0
x-1= 0x2-2= 0
x= 1x=±2

The used sign “” is the logical or.

Title zero rule of product
Canonical name ZeroRuleOfProduct
Date of creation 2013-03-22 15:06:46
Last modified on 2013-03-22 15:06:46
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 11
Author pahio (2872)
Entry type Result
Classification msc 13G05
Synonym product to zero rule
Related topic CancellationRing
Related topic EulersDerivationOfTheQuarticFormula
Related topic GroupingMethodForFactorizingPolynomials
Related topic HyperbolasOrthogonalToEllipses