THE QUADRATIC EQUATION

   

An equation of the form

            ax² + bx + c = 0

is known as the quadratic equation.  The values of x that satisfy the equation are known as the roots of the equation.  A quadratic equation has two roots which are given by the following two formulae:

                         -b  + sqrt(b² - 4ac)            

           root 1 = _______________

                             2a

                          -b  - sqrt(b² - 4ac)

           root 2 = ________________

                                    2a

A program to evaluate these roots is given in Fig.3.10. The program requests the user to input the values of a, b and c and outputs root1 and root2.

Program          

   #include  <math.h>                                         

                                                              

   main()                                                      

   {                                                          

      float  a, b, c, discriminant,                           

             root1, root2;                                    

                                                               

      printf("Input values of a, b, and c\n");                

      scanf("%f %f %f", &a, &b, &c);                          

                                                              

      discriminant = b*b - 4*a*c ;                            

                                                              

      if(discriminant < 0)                                    

         printf("\n\nROOTS ARE IMAGINARY\n");                 

      else                                                     

      {                                                       

         root1 = (-b + sqrt(discriminant))/(2.0*a);           

         root2 = (-b - sqrt(discriminant))/(2.0*a);           

         printf("\n\nRoot1 = %5.2f\n\nRoot2 = %5.2f\n",       

                     root1,root2 );                           

      }                                                       

   }  

                                                        

                                                               

Output                                                     

                                                              

   Input values of a, b, and c                                

   2 4 -16                                                     

                                                              

   Root1 =  2.00                                              

                                                              

   Root2 = -4.00                                               

                                                              

   Input values of a, b, and c                                

   1 2 3                                                      

                                          

   ROOTS ARE IMAGINARY