Question 673710
The Zero Product Property

The Zero Product Property simply states that if {{{ab = 0}}}, then either {{{a = 0}}} or {{{b = 0}}} (or {{{both}}}). 

A product of factors is {{{zero}}}{{{ if}}} and {{{only}}}{{{ if}}} one or more of the factors is zero.

This is particularly useful when solving quadratic equations. 

Example:

Suppose you want to solve the equation

{{{x^2 + x -20 = 0}}}

You can factor the left side as:

{{{(x + 5)(x-4) = 0}}}

Now, by the zero product property, either

{{{x + 5 = 0}}}   or  {{{ x -4 = 0}}},

which means either {{{x =-5}}} or {{{x = 4}}}. 

These are the two {{{solutions}}} of the equation.