The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.23: Using the Discriminant

The discriminant provides students with information about the number of solutions of a quadratic

equation. Students often make computationalmistakes when finding the discriminant or they

confuse the number of solutions if the discriminant is positive, negative, or zero.

1. Review the quadratic formula,x=

−b±

√

b^2 − 4 ac

2 a

, with your students.

2. Review the information and examples on the worksheet with your students. Emphasize that
   the expression inside the radical symbol,b^2 − 4 ac, is called the discriminant and can be
   evaluated by using the order of operations. Its value indicates the number of solutions to
   a quadratic equation. Note that the examples are written in standard form. Also explain the
   following:
   
   
   • There is one solution when the discriminant is 0. When 0 is substituted for the discrimi-
     nant in the quadratic formula,
     −b
     2 a
   
   
   
   

has only one value.

• There are two solutions if the discriminant is positive: the quantity−bplus the square
  root of the discriminant divided by 2aand the quantity−bminus the square root of the
  discriminate divided by 2a.


• There are no real solutions if the discriminant is negative. The square root of a negative
  number is not a real number.

EXTRA HELP:

Be sure that the equation is in standard form before you find the value of the discriminant.

ANSWER KEY:

(1)Two solutions (2)No real solutions (3)Two solutions (4)One solution

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(Challenge)It is important to find the discriminant before solving a quadratic equation because

the discriminant allows you to know how many solutions you are looking for.

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220 THE ALGEBRA TEACHER’S GUIDE