# Zero Product Principle

## Key Questions

• The Zero Product Principle says that if there is a product of two number that is equal to zero, than or the first, or the second (or both) has to be zero.

It is useful if an equation has to be solved.

e.g.: $\left(x - 5\right) \left(x + 6\right) \left(x - 3\right) = 0$ then: $x = 5 \mathmr{and} x = - 6 \mathmr{and} x = 3$

This Principle is true in all of the number systems studied in elementary mathematics.

• If $a \cdot b = 0$, then at least one of $a$ and $b$ must be zero since if $a$ and $b$ were nonzero, then $a \cdot b$ would be nonzero; therefore,

$a \cdot b = 0$ means that $a = 0$, $b = 0$, or both.

I hope that this was helpful.

• If two numbers are multiplied together and the answer is zero then either one of them is zero or both numbers are zero.