The Zero Product Property

The Zero Product Property simply states that if ab=0 , then either a=0orb=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 +x20=0 .

You can factor the left side as:

(x+5)(x4)=0

Now, by the zero product property, either

x+5=0   or   x4=0 ,

which means either x=5 or x=4 . These are the two solutions of the equation.