C program to find roots of Quadratic Equation

Before going to the program first let us understand what is a Quadratic Equation?

Quadratic Equation:

                                           A Quadratic Equation is any equation having the form: ax^2+bx+c=0

where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear equation, not quadratic.

For Example,

                        Quadratic Equation

For more understanding you can check out the following link:

https://www.mathsisfun.com/algebra/quadratic-equation.html

Program code to find roots of Quadratic Equation:

#include <stdio.h>
#include<conio.h>
#include <math.h>
void main()
{
    float a, b, c, determinant, r1,r2, real, imag;
    clrscr();
    printf("Enter coefficients a, b and c: ");
    scanf("%f%f%f",&a,&b,&c);
    determinant=b*b-4*a*c;
    if (determinant>0)
    {
        r1= (-b+sqrt(determinant))/(2*a);
        r2= (-b-sqrt(determinant))/(2*a);
        printf("Roots are: %.2f and %.2f",r1 , r2);
    }
    else if (determinant==0)
    {
        r1 = r2 = -b/(2*a);
        printf("Roots are: %.2f and %.2f", r1, r2);
    }
    else
    {
        real= -b/(2*a);
        imag = sqrt(-determinant)/(2*a);
        printf("Roots are: %.2f+%.2fi and %.2f-%.2fi", real, imag, real, imag);
    }
    getch();
}

Step by Step working of the above Program Code:

  1. First the computer reads the coefficients a , b and c from the user.
  2. Then it computes the value of determinant using the formula.

determinant=b*b-4*a*c;

  1. Then checks the determinant value is greater than , equal or less than to zero using if else if ladder.
  2. If the determinant value is greater than zero, then root1 and root2 value is calculated using the formula:

r1=(-b+sqrt(determinant))/(2*a)

r2=(-b-sqrt(determinant))/(2*a)

  1. If the determinant value is equal to zero, then root1 and root2 value is calculated using the formula:

r1=r2=-b/(2*a)

  1. If the determinant value is less than zero, then root1 and root2 value is calculated using the formula:

real=-b/(2*a)

imag=sqrt(-determinant)/(2*a)

  1. Finally print the roots of the quadratic equation.

Output:

quadratic equation

quadratic equation

TO DOWNLOAD THE PROGRAM CODE :CLICK HERE

 

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