Introducing the Zero Product Property

8.4.1 Introducing the Zero Product Property

8.4.1 • Introducing the Zero Product Property

What values of the variables make each equation true?

Find the value of $a$ .

$6 + 2 a = 0$

$- 3$

Find the value of $b$ .

$7 b = 0$

$0$

Find the value of $c$ .

$7 (c - 5) = 0$

$3$

Determine which of the statements are true if $g \cdot h = 0$ . HINT: There may be more than one statement that is true.

$(g =)$ . In other words, $g$ equals zero and $h$ may be any real number.
$g = h = 0$ . In other words, both $g$ and $h$ are equal to zero.
$h = 0$ . In other words, $h$ equals zero and $g$ may be any real number.
$g \neq 0$ , $h \neq 0$ . In other words, neither $g$ nor $h$ are equal to zero.

What did you notice about one of the factors in each of the previous problems?

Compare your answer:

At least one of the factors in each equation was 0 or equivalent to 0.

We will use the zero product property to help solve quadratic equations throughout this lesson.

If the product of two expressions is 0, then one or both of the expressions equal 0.

If $a b = 0$ , then $a = 0$ or $b = 0$ , or $a = b = 0$ .