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10.6: The Discriminant

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

At the end of this lesson, students will be able to:

  • Find the discriminant of a quadratic equation.
  • Interpret the discriminant of a quadratic equation.
  • Solve real-world problems using quadratic functions and interpreting the discriminant.

Vocabulary

Terms introduced in this lesson:

discriminant
double root
nature of solutions
distinct real solutions
non-real solutions
rational number solutions
irrational number solutions

Teaching Strategies and Tips

In this lesson, students learn that each quadratic equation is associated with a number whose sign tells how many solutions there are to that equation.

  • Emphasize that the equation does not have to be solved.

Point out that if the discriminant is not a perfect square, then the solutions are irrational numbers. See Example 3.

Use Examples 5-7 to illustrate how useful interpreting the discriminant in context of the problem can be.

Error Troubleshooting

General Tip: Remind students to use care when substituting values into the discriminant.

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CK.MAT.ENG.TE.1.Algebra-I.10.6