Programming Example 1: Quadratic Equation Solver

Problem Statement

Given a quadratic equation as follows:

if b*b-4*a*c is non-negative, the roots of the equation can be solved with the following formulae:

Write a program to read in the coefficients a, b and c, and compute and display the roots. If the discriminant b*b - 4*a*c is negative, the equation has complex root. Thus, this program should solve the equation if the discriminant is non-negative and show a message otherwise.

Solution

! ---------------------------------------------------
!   Solve  Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0
!   Now, we are able to detect complex roots.
! ---------------------------------------------------

PROGRAM  QuadraticEquation
   IMPLICIT  NONE

   REAL  :: a, b, c
   REAL  :: d
   REAL  :: root1, root2

!  read in the coefficients a, b and c

   READ(*,*)  a, b, c
   WRITE(*,*) 'a = ', a
   WRITE(*,*) 'b = ', b
   WRITE(*,*) 'c = ', c
   WRITE(*,*)

!  compute the square root of discriminant d

   d = b*b - 4.0*a*c
   IF (d >= 0.0) THEN              ! is it solvable?
      d     = SQRT(d)
      root1 = (-b + d)/(2.0*a)     ! first root
      root2 = (-b - d)/(2.0*a)     ! second root
      WRITE(*,*)  'Roots are ', root1, ' and ', root2
   ELSE                            ! complex roots
      WRITE(*,*)  'There is no real roots!'
      WRITE(*,*)  'Discriminant = ', d
   END IF

END PROGRAM  QuadraticEquation

Click here to download this program.

Program Input and Output

If the input to the program consists of 1.0, 5.0 and 2.0, we have the following output. Since the discriminant is b*b - 4.0*a*c = 5.0*5.0 - 4.0*1.0*2.0 = 17.0 > 0.0, the THEN part is executed and the real roots are -0.438447237 and -4.561553.
```
1.0  5.0  2.0

a = 1.
b = 5.
c = 2.

Roots are -0.438447237 and -4.561553
```
If the input to the program consists of 1.0, 2.0 and 5.0, we have the following output. Since the discriminant is b*b - 4.0*a*c = 2.0*2.0 - 4.0*1.0*5.0 = -16.0 < 0.0, the ELSE part is executed and a message of no real roots is displayed followed the value of the discriminant.
```
1.0  2.0  5.0

a = 1.
b = 2.
c = 5.

There is no real roots!
Discriminant = -16.
```

Discussion

Here is the box trick of this program. Note that information in different parts of the box do not have to be very precise. As long as it can tell what to do, it would be sufficient.

*bb - 4.0ac >= 0.0**	computes the real roots
	there is no real roots