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Lesson 2

1. Lesson 2

1.8. Explore 4

Mathematics 20-1 Module 4

Module 4: Quadratic Equations and Inequalities

 

Zero-Product Property

 

In the cartoon in Discover, the girl was able to guess that one of the two integers was zero based on the clue that the product of the two integers was zero. This is an example of the zero-product property.

 

If the product of two or more numbers is zero, the value of at least one of those factors is zero. For example, if a × b = 0, one of the following must be true:

  • a = 0

  • b = 0

  • both a = 0  and b = 0
This is a play button that opens Zero-Product Property in Action.

The zero-product property is a key idea in solving quadratic equations by factoring. Watch Zero-Product Property in Action to see why. Before you begin watching, retrieve your work from Try This 1. Compare the process you used with what you see in the video.

 



In the last lesson you learned that the solution of a quadratic equation could contain one root, two roots, or no roots. In the next part of the lesson you will investigate the relationship between the factored form of a quadratic equation and the number of roots in the solution.



textbook

Turn to “Example 3” on pages 223 to 225 in the textbook. Work through the example, paying attention to the following:

  • the reasoning for each step

  • the different factoring methods presented

  • the number of distinct roots in each solution

Complete Try This 3 based on what you have read. You will find some of the same equations that you encountered in the textbook. Keep your textbook handy in case you need to refer to those pages.

 

Try This 3

 

For each of the quadratic equations in the first column, graph the corresponding quadratic function and indicate the number of distinct roots. Then express the quadratic equation in factored form.

 

Note: You may encounter quadratic equations that cannot be factored normally. In those cases, you can write “Not factorable.”

 

 
Quadratic Equation Solution by Graphing Number of Distinct Roots Solution by Factoring
x2 + 6x + 9 = 0      
2x2 − 9x − 5 = 0      
2x2 + 4 = 0      
2x2 + 2x + 1 = 0      

 

Share 2

 

With a classmate, share and compare your charts from Try This 3, and then discuss the following questions.

  1. How can you tell from the factored form of a quadratic equation whether the equation has one, two, or no roots?

  2. When will a quadratic equation not have roots? Explain this situation in terms of the graph of the function and the ability to factor the equation.

course folder Save your responses in your course folder.