Quadratic function 

1. Definition:


The quadratic function ax2 + bx + c is a polynomial of degree 2 
(second order). The related equation ax2 + bx + c = 0 has two solutions.
We are interested in calculating the roots of this equation. If a is null, 
we have a linear equation and the solution is -c/b. If the discriminant 
is negative, we have imaginary roots: x1,2= (-b -,+ (b*b - 4*a*c)i/(2*a), 
and if the discriminant is positive, we have real roots: 
x1,2= (- b +,- sqrt(b*b - 4*a*c)/(2*a).


2. The method in Fortran90 language:

PROGRAM quadratic_equation
IMPLICIT NONE
REAL :: a,b,c, disc, x1, x2
PRINT*,"Enter the values of the coefficients a, b, c : --> \n"
READ*, a,b,c

disc=b*b-4*a*c

IF (a == 0) THEN
PRINT*,"The equation is linear and the related solution is:"
PRINT*,"x0 = ", -c/b

ELSE IF(disc <0) THEN
x1 = -b/2*a
x2 = SQRT(- disc)/2*a
PRINT*,"\n The roots are complexe: "
PRINT*,"x1 = ",x1," + ",x2,"i"
PRINT*,"x2 = ",x1," - ",x2,"i"

ELSE
x1 = (-b + SQRT(disc))/2*a
x2 = (-b - SQRT(disc))/2*a
PRINT*,"\n The roots are real:"
PRINT*,"x1 = ",x1
PRINT*,"x2 = ",x2
ENDIF
END PROGRAM quadratic_equation