The Discriminant

                  Lesson 1

                                                                                                                       

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

If discriminant:

         b - 4ac > 0 : Roots are real

         b - 4ac = 0 : Roots are equal

         b - 4ac < 0 : Roots are complex and imaginary

         b - 4ac is a perfect square : Roots are rational

 

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

x + 2x + 3=0        

  

                                                    Solution      Discriminant = b - 4ac             

                                                    Step 1:                      

                                      

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

                                                    Step 2:                                                                             

                                                                                 

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

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

 

                                                    Solution b - 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.

x2+2x+11=0

B.

i2+3i-2=0

 

        

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