Zero Product Rule for Quadratic Equations

Definition:

The Zero Product Rule says that when the product of two terms is zero, then either of the terms is equal to zero.

Simple definition:

When we multiply two variables, terms or expressions, and the result is zero, then either of the two variables/terms/expression is itself equal to zero.

For example, in the adjoining picture, it is shown that when you multiply 'a' and 'b', the result is zero. Hence we conclude that either a equals 0 or b equals 0.

Example:

If (x + 2)(x + 3) = 0, then by the Zero Product Rule,

• Either (x + 2) = 0
• Or (x + 3) = 0

Solving Quadratic Equations by Zero Product Rule

Quadratic expressions can be factored to a product of two linear expressions. Thus if in a quadratic equation, a quadratic expression is equated to zero, then the product of two linear expressions can be equated to zero. By applying the zero product rule, either of the two linear expressions is equal to zero.

An example:

In the quadratic equation x² + 6x + 8 = 0, the left hand side can be factored to (x + 4)(x + 2)

Thus (x + 2)(x + 4) = 0. Applying the Zero Product Rule,

• Either x + 2 = 0; then x = -2
• Or x + 4 = 0; then x = -4

Thus the roots of the quadratic equation are -2 and -4.