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# 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 .

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Example:
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Suppose you want to solve the equation

${x}^{2}+x-20=0$ .

You can factor the left side as:

$(x+5)(x-4)=0$

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.