# The Zero Product Property

The Zero Product Property simply states that if $ab=0$ , then either $a=0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}b=0$(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:

$\left(x+5\right)\left(x-4\right)=0$

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.