/* program to illustrate 4 functions related to the quadratic formula 
   given a, b, and c, the formula computes solutions to
      a * x^2 +b * x + c = 0
   if discriminant = sqrt (b*b - 4*a*c), a != 0, and discriminant > 0,
   then the two real solutions of this equation are
     (-b + discriminant) / (2.0 * a)
  and
     (-b - discriminant) / (2.0 * a)

  Note: When compiling, link with the math library using the "-lm" flag. E.g.,
          cc -lm -o quadratic quadratic.c
*/

#include <stdio.h>
#include <math.h>

/* Print a quadratic equation given the coefficients. */
void
printEquation (double coeff2, double coeff1, double coeff0)
{
  printf ("Equation:  %lf*x^2 + %lf*x + %lf = 0\n", coeff2, coeff1, coeff0);
} // printEquation


/* Compute the discriminant of a quadratic equation 
 *   r*x^2 + s*x + t = 0 given the coefficients r, s, and t.
*  
*  Precondition:
*    s*s >= 4*r*t
*  Postcondition:
*    returns the square root of s*s - 4*r*t
*/
double
computeDiscriminant (double r, double s, double t)
{
  return sqrt (s*s - 4*r*t);
} // computeDiscriminant


/* Print both roots of a quadratic equation a*x^2 + b*x + c = 0.
 *
 * Preconditions:
 *   Both roots must be real
 *   a != 0
 */
void
printRoots (double a, double b, double c)
{
  double discriminant = computeDiscriminant (a, b, c);
  double root1 =  (-b + discriminant) / (2.0 * a);
  double root2 =  (-b - discriminant) / (2.0 * a);

  printf ("    Roots:  %lf and %lf\n", root1, root2);
} // printRoots


/* Control processing for x^2 - 3*x + 2.0 = 0: prints equation and its roots */
void
displayExample1 (void)
{
  printEquation (1.0, -3.0, 2.0);
  printRoots (1.0, -3.0, 2.0);
} // displayExample1


/* Control processing for 2.0*x^2 - 7.0*x - 4.0 = 0; 
 * prints equation and its roots */
void
displayExample2 (void)
{
  printEquation (2.0, -7.0, -4.0);
  printRoots (2.0, -7.0, -4.0);
} // displayExample2


/* Main function illustrating two equations with their solution via the 
 * quadratic formula */
int
main (void)
{
  printf ("program illustrating functions and the quadratic formula\n");

  displayExample1();
  displayExample2();

  return 0;
} // main