Objective 14 – Null Factor Law and Solving Quadratic Equations:

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Objective 14 – Null Factor Law and Solving Quadratic Equations:

What is the null factor law?

Given that

Then either

:

AB

A

0

0 or

B

0

Why is this important to know?

We will use the null factor law to solve quadratic equations.

Ex: Solve for x:

x

2

x

72

0

In this problem it is hard to isolate x. However if we factor the left hand side of the equation we create a situation where we are multiplying two things together that equals zero:

x

2

x

72

(

x

9 )(

x

8 )

0

0

Now we will apply the null factor law: (

 means therefore

x

2

x

72

0

(

x

 either

9 )(

x

(

x

9 )

8 )

0

0 or (

x

8 )

0

)

To finish the problem we must solve for x in each equation:

x

2

x

72

(

x

9 )(

x

8 )

0

0

 either (

x

9 )

0 or (

x

8 )

0

x

 

9 or

x

8

What do the answers

x x

 

9 and

x

8 mean to the problem?

9 and

x

8 are the values of

x

that make the equation true let

x

 

9

x

2

x

72

0 let

x

8

x

2

x

72

0

(

9 )

2

(

9 )

81

81

0

72

0

0

0 This is true and

( 8 )

2

( 8 )

72

72

72

0

0

0

0 This is true

More Examples:

x

2

x

0

x

(

x

a)

 either

x

1 )

0 or

x

0

1

0

x

0 or

x

 

1

9

x

3

x

0

(

x

)( 9

x

2

1 )

0 b) (

x

)( 3

x

 either

x

1 )( 3

x

1 )

0 or 3

x

1

0

0 or 3

x

1

0

x

0 or

x

 

1

3 or

x

1

3

x

2

12

x

11

0

( c)

 either

x x

11

11 )(

x

1 )

0 or

x

0

1

x

-11 or

x

 

1

0

2

x

2

x

6

0

2

x

2

4

x

3

x

6

0 d)

( 2

x

)(

x

(

x

2

2 )( 2

x

)

3

3 (

x

)

2 )

0

0

 either

x

2

0 or 2

x

3

0

x

-2 or

x

3

2

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