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

Name Date

WORKSHEET 5.23: USING THE DISCRIMINANT

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The discriminant,b^2 − 4 ac, is the expression that is inside the radical symbol in the quadratic

formula,x=

−b±

√

b^2 − 4 ac

2 a

. The discriminant can be used to determine the number of

solutions of a quadratic equation expressed in standard form asax^2 +bx+c= 0 , where

a= 0. Use the guidelines below:

1. Write the equation in standard form, if necessary.


2. Identify the values ofa,b,andc.


3. Substitute these values in the discriminant and use the order of operations to find the
   value of the discriminant.
   
   
   • If the value of the discriminant is 0, the equation has one solution.
   
   
   • If the value of the discriminant is positive, the equation has two solutions.
   
   
   • If the value of the discriminant is negative, the equation has no real solutions.
   
   
   
   

Example 1 Example 2 Example 3

x^2 − 4 x+ 4 = 0 x^2 + 5 x+ 3 = 02 x^2 +x+ 5 = 0

a=1,b=−4,c= 4 a=1,b=5,c= 3 a=2,b=1,c= 5

(−4)^2 −4(1)(4) 52 −4(1)(3) 12 −4(2)(5)

16 − 625 − 12 1 − 40

013 − 39

There is one solution. There are two solutions. There are no real solutions.

DIRECTIONS: Use the discriminant to determine the number of solutions. If there are no

real solutions, write ‘‘no real solutions.’’

1. x^2 + 6 x− 5 = 0 2. x^2 − 4 x+ 10 = 0


2. x^2 − 2 x− 3 = 0 4. x^2 + 6 x=− 9

CHALLENGE:Why is finding the discriminant an important step to take before

solving an equation?

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©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.