# If #ab=0#, what is true of #a# or #b#?

##### 1 Answer

Aug 19, 2014

This property is used frequently to solve problems, even ones that are very complex.

A problem could be as easy as a factored quadratic:

#(x-3)(x+2)=0#

So:

#x-3=0#

#x=3#

or

#x+2=0#

#x=-2#

Or it could be more complicated like:

#(sin x-1/2)(cos x+1/sqrt(2))=0#

So:

#sin x-1/2=0#

#sin x = 1/2#

#x=pi/6+2pi n, n in ZZ#

#x=(5 pi)/6+2pi n, n in ZZ#

or

#cos x+1/sqrt(2)=0#

#cos x=-1/sqrt(2)#

#x=(3pi)/4+pi n, n in ZZ#

As you can see, the zero factor property allows us to algebraically solve many math problems.