The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0. In other words, if then either or . This property is handy when an equation we want to solve states that the product of two factors is 0.

Suppose we want to solve . This equation says that the product of and is 0. For this to be true, either or , so both 0 and -9 are solutions.

Here is another equation: . The equation says the product of and is 0, so we can use the zero product property to help us find the values of . For the equation to be true, one of the factors must be 0.

• For to be true, would have to be 2.345.
• For or ( ) to be true, would have to be , or .

The solutions are 2.345 and .

In general, when a quadratic expression in factored form is on one side of an equation and 0 is on the other side, we can use the zero product property to find its solutions.

This property is unique to 0. Given an equation like , the factors could be 2 and 3, 1 and 6, -12 and ,  and , or any other of the infinite number of combinations. This type of equation does not give insight into the value of  or .