The Discriminant

                  Lesson 1

                                                    In a quadratic equation (ax²+bx+c=0), discriminant is given as b² - 4ac

If discriminant:

· b² - 4ac > 0 : Roots are real

· b² - 4ac = 0 : Roots are equal

· b² - 4ac < 0 : Roots are complex and imaginary

· b² - 4ac is a perfect square : Roots are rational

Problem:   Find the nature of the roots of the equation:

x² + 2x + 3=0

Solution    Discriminant = b² - 4ac

Step 1:                      

Solution Here, a=1; b= 2; c= 3

                                                    Step 2:                                  

Solution      Discriminant = (2)² - {4x1x (3)}

Step 3:     Discriminant = 4 – {4x (3)} = 4 - 12 Discriminant = -8    

                                                    Solution b² - 4ac < 0; Roots are complex and imaginary                  

                                                    Step 4:    

                                                    Solution    Answer: Roots are complex and imaginary

                                                    Step 5:                                                                      

                                                    Complete

Try two practice problems:  

Do the following:                                                                                      

Find the nature of roots of the following quadratic equations:
A.	x^2+2x+11=0	B.	i^2+3i-2=0

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