Quardratic Equations

Quadratic equations with real coefficients:

An equation of the form
                                     

where    is called a quadratic equation with real coefficients whose roots are

        

The quantity       is known as discriminant.

• The roots are real and distinct if  .
• The roots are real and equal if  
• The roots are complex if  .

Relations between roots and coefficients

                                          

                                                       

Formation of quadratic equations with given roots

If     are the roots then quadratic equation is

By symmetric function of roots, we mean that the function remains unchanged when the roots are interchanged.