C program Roots or solution of Quadratic Equation

It has two C programs, they are

1. function of quadratic equation -

   A value x is input and f(x) is output of the program.

2. solving a quadratic equation -

   The coefficients a,b and c values are input and the solution value x1 and x2 are output of the program.

Function of x to Quadratic equation

The quadratic equation formed by three coefficients a,b and c are set constant in the program and a input x value is read from user to find f(x) (function of x).

            y =f(x) = ax 2 + bx + c 
     
         it is a quadratic function, find y =? of given x value
         Given : a=1.0,b=2.0,c=1.0  and x = 0.5              
          substitute the given into quadratic function.

          y  =  1 * 0.5 2 + 2*0.5 + 1
             =  1 * 0.25 + 1 +1
             =  0.25 + 2
   y= f(0.5) = 2.25             

   

Function of x to Quadratic equation - C program

The C program finds function of x for given a input x. The input x c values is read from user while the program is running and then prints function of x as results of the program.

 
#include <stdio.h>
#include <string.h>

int main() {

   const float a=1.0,b=2.0,c=1.0; 
   float x,fx;
   printf ("\n Find  f(x) of given x from quadratic equation");
   
   printf("\n Enter x value  :" );
   scanf("%f", &x);
   
   fx = a*x*x + b*x + c;

   printf("\n Result ");   
   printf("\nx = %.2f ",x);
   printf("\nf(x) = %.2f ",fx);           
   return 0;
}

 

Quadratic equation - C program Output

 Find  f(x) of given x from quadratic equation
 Enter x value 
 2.5

Result 
 x =2.0
 f(x) =9.00

Solution of quadratic equation

Quadratic equation

A quadratic equation is formed by 3 coefficients a,b and c. if we know values of these coefficients, we can solve it by finding roots of the equation.

Solution of quadratic equation

The solution x for a quadratic equation derived from this following formulae. The coefficients a,b and c values are substitute into this formula to obtain solution x.

if the sqrt has positive value, then solution x will be real number, otherwise the solution will be complex number.

Roots of Quadratic Equation - C program

The C program finds solution or roots of a given quadratic function. The coefficients a,b and c values is read from user while the program is running and then prints solution x as results of the program.

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

int main() {

   float a,b,c; 
   char xtmp[50],x2tmp[50];   
   printf ("\n Find  roots of the quadratic equation");
   
   printf("\n Enter a value  :" );
   scanf("%f", &a);
   printf("\n Enter b value  :" );
   scanf("%f", &b);
   printf("\n Enter c value  :" );
   scanf("%f", &c);
         
    float tmp =b*b - 4*a*c;
    float tmp2 = 2.0*a;     
          
    if ( tmp>0 ) {      
   double x1  =  (-b + sqrt(tmp) ) / tmp2;
   double x2  =  (-b - sqrt(tmp) ) / tmp2;
   printf(" Root of the Equation is x1=%.2f x2=%.2f" ,x1,x2 );
 } 
 else {          
    sprintf(xtmp,"%.2f+sqrt(%.2f)i/(2*%.2f)",-b,tmp,a);
    sprintf(x2tmp,"%.2f-sqrt(%.2f)i/(2*%.2f)",-b,tmp,a);    
    printf("Root of the Equation is x= %s \n %s" , xtmp , x2tmp );      
 }                  
   return 0;
}

Roots or solution of Quadratic Equation - Output

 Find  roots of the quadratic equation

 Enter a value 5
 Enter b value 6
 Enter c value 1

 Root of the Equation is x1 = -0.20, x2=-1 

Download c program source code

• Function of x to Quadratic equation


• Solution of Quadratic Equation