/*
 *  ======================================================================
 *  Solve Quadratic Equations : Coefficients are read in from keyboard
 *                            : Roots of Quadratic are printed to screen.
 *                                                                     
 *  Note : Naive implementation of quadratic equation solver. This algorithm
 *         does not take into account possible loss of accuracy when two
 *         floating point numbers of almost equal size are subtracted.
 *  ======================================================================
 */

#include <stdio.h>   /* Standard Input/Output function declarations */
#include <math.h>    /* Math functions, such as sqrt(x).            */

float discriminant( float , float , float );

int main( void ) {
float     fA, fB, fC;          /* Coefficients for Quadratic Equation      */
float fRoot1, fRoot2;          /* Real Roots 1 and 2 of Quadratic Equation */
float  fDiscriminant;          /* Discriminant of Quadratic                */
char     caBuffer[8];          /* Buffer array to hold input from screen   */

 /* [a] : Print Welcome Message */

    printf("Welcome to the Quadratic Equation Solver (Version 1)\n");
    printf("====================================================\n");

 /* [b] : Read in Set of Equations */

    printf("\nWould you like to input a quadratic quations (yes/no/quit) ? ");

    scanf("%s%*c", caBuffer);
    if(strcmp(caBuffer,"yes") != 0)
       exit (1);

 /* [c] : Prompt User for Coefficents of Quadratic Equation */

    printf("Please enter coefficients for equation a.x^2 + b.x + c\n");
    printf("Enter coefficient a : ");
    scanf("%f%*c", &fA);
    printf("Enter coefficient b : ");
    scanf("%f%*c", &fB);
    printf("Enter coefficient c : ");
    scanf("%f%*c", &fC);

 /* [d] : Print Quadratic Equation to Screen */

    printf("Equation you have entered is : %g.x^2 + %g.x + %g\n", fA, fB, fC);

 /* [e] : Compute Roots of simplified equations : fA equals zero */

    if(fA == 0 && fB == 0) {
       printf("Cannot Solve Extremely Degenerate Equation %14.8g = 0.0\n", fC );
       exit (1);
    }

    if(fA == 0 && fB != 0) {
       fRoot1 = - fC/fB;
       printf("Degenerate Root : Root = %14.8g\n", fRoot1 );
       exit (1);
    }

 /* [f] : Compute Roots of Quadratic Equation : fA not equal to zero */

    fDiscriminant = discriminant( fA, fB, fC );
    if(fDiscriminant >= 0) { /* Case for Two Real Roots */

       fRoot1 = -fB/2.0/fA - sqrt( fDiscriminant )/2.0/fA;
       fRoot2 = -fB/2.0/fA + sqrt( fDiscriminant )/2.0/fA;

       printf("Two Real Roots : Root1 = %14.8g\n", fRoot1 );
       printf("               : Root2 = %14.8g\n", fRoot2 );
    } else {                   /* Case for Complex Roots */

       printf("Two Complex Roots : Root1 = %14.8g + %14.8g i\n", -fB/2.0/fA,
               sqrt( -fDiscriminant )/2.0/fA);
       printf("                  : Root2 = %14.8g + %14.8g i\n", -fB/2.0/fA,
              -sqrt( -fDiscriminant )/2.0/fA);
    }
}

/*
 *  ======================================================
 *  Function to Compute Discriminant of Quadratic Equation
 *  ======================================================
 */

float discriminant( float fA, float fB, float fC ) {
      return(fB*fB - 4.0*fA*fC);
}