/* ---------------------------------------------------------------------  
// Figure 5.10 and 5.11:  Quadratic roots.
//    Solve a quadratic equation with any coefficients a, b, and c.  
//    Test for degenerate equations and account for single roots and 
//    complex roots.
// ------------------------------------------------------------------------ 
*/
#include "tools.h" 

void main( void )              
{                
    double a, b, c;                    /* Coefficients of the equation. */
    double d, two_a, sroot;            /* Working storage. */
    double xreal, ximag, x1, x2;       /* Answers. */

    banner();                   
    puts( " Find the roots of ax*x + bx + c = 0" );      
    printf( " Enter the values of a, b, and c: " );
    scanf( "%lg%lg%lg", &a, &b, &c ); 
    printf( "\n The equation is  %g *x*x + %g *x + %g = 0\n", a, b, c );

    if (a == 0 && b == 0) {
        printf( " Degenerate equation -- no roots\n" );
    }
    else if (a == 0) {
        printf( " Linear equation -- root at -c/b = %g\n", -c/b );
    }
    else {
        two_a = 2 * a;  
        d = b * b - 4  *a * c;     /* discriminant of equation. */               
        sroot = sqrt( fabs(d) );   /* fabs is floating point absolute value. */               
        if (d < 0) {               /* If d is negative the roots are complex. */                                                  
            xreal = -b / two_a;                              
            ximag = sroot / two_a;      
            printf( "\n The roots are x = %g + %g i and x = %g - %g i \n", 
                    xreal, ximag, xreal, ximag );       
        }   
        else if (d == 0) {          /* There is only one root. */                   
            printf( "\n Single real root at x = %g \n", -b / two_a );
        }
        else {                      /* If d is positive the roots are real. */                                                 
            x1 = -b / two_a + sroot / two_a;            
            x2 = -b / two_a - sroot / two_a;            
            printf( "\n The real roots are x = %g and %g \n", x1, x2 );
        }
    }
    bye();
}