C Program to find the roots of quadratic equation

Quadratic equations are the polynomial equation with degree 2. It is represented as ax² + bx +c = 0, where a, b and c are the coefficient variable of the equation. The universal rule of quadratic equation defines that the value of 'a' cannot be zero, and the value of x is used to find the roots of the quadratic equation (a, b). A quadratic equation's roots are defined in three ways: real and distinct, real and equal, and real and imaginary.

Nature of the roots

The nature of the roots depends on the Discriminant (D) where D is.

If D > 0, the roots are real and distinct (unequal)
If D = 0, the roots are real and equal.
If D < 0, the roots are real and imaginary.

Steps to find the square roots of the quadratic equation

Initialize all the variables used in the quadratic equation.
Take inputs of all coefficient variables x, y and z from the user.
And then, find the discriminant of the quadratic equation using the formula:
Discriminant = (y * y) - (4 * x *z).
Calculate the roots based on the nature of the discriminant of the quadratic equation.
If discriminant > 0, then
Root1 = (-y + sqrt(det)) / (2 * x)
Root2 = (-y + sqrt(det)) / (2 * x)
Print the roots are real and distinct.
Else if (discriminant = 0) then,
Root1 = Root2 = -y / (2 * x).
Print both roots are real and equal.
Else (discriminant < 0), the roots are distinct complex where,
Real part of the root is: Root1 = Root2 = -y / (2 * x) or real = -y / (2 * x).
Imaginary part of the root is: sqrt( -discriminant) / (2 * x).
Print both roots are imaginary, where first root is (r + i) img and second root is (r - i) img.
Exit or terminate the program.

Pseudo Code of the Quadratic Equation

Start
Input the coefficient variable, x, y and z.
D <- sqrt (y * y - 4 * x * z).
R1 <- (-y + D) / ( 2 * x).
R2 <- (-y - D) / (2 * x).
Print the roots R1 and R2.
Stop

Let's implements the above steps in a C program to find the roots of the quadratic equation.

/* C Program to Find the Roots of the Quadratic Equation */
#include<stdio.h>
#include<math.h>  // it is used for math calculation
#include<conio.h>
void main()
{
	float x, y, z, det, root1, root2, real, img;
	printf("\n Enter the value of coefficient x, y and z: \n ");
	scanf("%f %f %f", &x, &y, &z);
	// define the quadratic formula of the nature of the root
	det = y * y - 4 * x * z;	
	// defines the conditions for real and different roots of the quadratic equation
	if (det > 0)
	{
	root1 = (-y + sqrt(det)) / (2 * x);
	root2 = (-y + sqrt(det)) / (2 * x);
	printf("\n Value of root1 = %.2f and value of root2 = %.2f", root1, root2);
	}
	// elseif condition defines both roots ( real and equal root) are equal in the quadratic equation
	else if (det == 0)
	{
		root1 = root2 = -y / (2 * x); // both roots are equal;
		printf("\n Value of root1 = %.2f and Value of root2 = %.2f", root1, root2);
	}
	// if det < 0, means both roots are real and imaginary in the quadratic equation.
	else {
		real = -y / (2 * x);
		img = sqrt(-det) / (2 * x);
		printf("\n value of root1 = %.2f + %.2fi and value of root2 = %.2f - %.2fi ", real, img, real, img);
	}
	getch();
	}

Output:

Let's create another C program in which we have used function.

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

// use function to check the nature of the roots in the quadratic equation
void R_Quadratic( int x, int y, int z)
{
	if (x == 0) // Checks the vakue of x, if x = 0, the equation is not quadratic equation.
	{
		printf(" The value of x cannot be zero");
		return;
	}
	int det = y * y - 4 * x * z;
	double sqrt_det = sqrt(abs (det));
	if (det > 0)
	{
	printf("\n Both roots are real and different \n ");
	printf("%.2f\n %.2f", (double) (-y + sqrt_det) / (2 * x), (double) (-y - sqrt_det) / (2 * x));
		}
else if (det == 0)
{
	printf("\n Both roots are real and same ");
	printf("%.2f", -(double)y / (2 * x));
}
else
{
	printf("\n Both roots are complex");
	printf("\n %.2f + %.2fi \n%.2f - %.2fi", -(double)y / (2 * x), sqrt_det, -(double)y / (2 * x), sqrt_det);
	
}
}
void main()
{
	int x, y, z; // declare variables x, y and z
	printf("\n Enter the value of coefficient x, y and z: ");
	scanf("%d %d %d", &x, &y, &z);
	R_Quadratic(x, y, z);  // call function R_Quadratic()
	getch();
}

Output: