Zero product property

The zero product property states that for any real numbers a and b, if ab = 0, then either a equals zero, b equals zero, or both a and b equal zero.

Example #1

If 6 × b = 0, then b must be zero since 6 is not equal to zero.

Example #2

If a × 10 = 0, then a must be zero since 10 is not equal to zero.

Example #3:

If a × b × 2   = 0, then we can have any of the following 3 situations:

0 × b × 2   = 0 ( a = 0 )

a × 0 × 2   = 0 ( b = 0 )

0 × 0 × 2   = 0 (a = 0 and b = 0)

Zero product property and quadratic equations

The zero product property is often used when solving quadratic equations by factoring.

For example, solve x2 + 8x - 20 = 0

x2 + 8x - 20 = 0      (Original equation)

(x - 2)(x + 10) = 0   (Factored form)

x - 2 = 0  or x + 10 = 0   (Zero product property)

x = 2     or x = -10

The solutions of the equation are 2 and -10.

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