Math Doubts

Zero Product property


A product rule of two or more factors when its product equals to zero is called zero product property.


The product of two or more factors is zero in some cases. It is possible mathematically if at least one of them is equal to zero. The property is used as a rule in mathematics to find the values of the variables.


$a$ and $b$ are two factors and the product of them is equal to zero.

$a \times b \,=\, 0$

There are two possibilities for the product of two factors to become zero.

  1. If $a \,=\, 0$, then $0 \times b \,=\, 0$.
  2. If $b \,=\, 0$, then $a \times 0 \,=\, 0$.

In this case, either $a$ or $b$ is equal to zero. Therefore, $a$ is equal to zero or $b$ is equal to zero, is known as zero product property.

$\therefore \,\,\,\,\,\, a \,=\, 0 \,\,\,$ or $\,\,\, b \,=\, 0$

The rule of zero product property is not limited to two factors and can also be applied to more than two factors as well.

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