In this blog post, we learn how to write a C program to find the roots of a quadratic equation?. We will write the C program to find the roots of a quadratic equation using the if-else condition. Write C program to find roots of quadratic equation using switch statements. How to find all roots of a quadratic equation using if else in C programming. Logic to find roots of quadratic equation in C programming.
Let see an example,
Input : a = 1, b = -2, c = 1
Output: Roots are real and same
1
Input : a = 1, b = 7, c = 12
Output: Roots are real and different
-3, -4
Input : a = 1, b = 1, c = 1
Output : Roots are complex
-0.5 + i1.73205
-0.5 - i1.73205
Quadratic equation:
In algebra, a quadratic equation is an equation that can be rearranged in standard form as,
ax2 + bx + c = 0
Below is a direct formula for finding the roots of the quadratic equation.
There are the following important cases of this formula.
Case 1: (Discriminant < 0)
b*b < 4*a*c, then roots are complex(not real). For example roots of x2 + x + 1, roots are -0.5 + i1.73205 and -0.5 - i1.73205
Case 2: (Discriminant == 0)
b*b == 4*a*c, then roots are real and both roots are the same. For example, roots of x2 - 2x + 1 are 1 and 1
Case 3 (Discriminant > 0):
b*b > 4*a*c, then roots are real and different. For example, roots of x2 - 7x - 12 are 3 and 4
C Program to Find the Roots of a Quadratic Equation using if-else:
The below program ask the user to enter the value of a,b and c. After getting the value from the user it will calculate on the basis of ‘Discriminant’ value.
#include <stdio.h>
#include <math.h>
int main()
{
float a, b, c;
float root1, root2, imaginary;
float discriminant;
printf("Enter value of a of quadratic equation (aX^2 + bX + c): ");
scanf("%f", &a);
printf("Enter value of b of quadratic equation (aX^2 + bX + c): ");
scanf("%f",&b);
printf("Enter values of c of quadratic equation (aX^2 + bX + c): ");
scanf("%f",&c);
// Find discriminant of the equation
discriminant = (b * b) - (4 * a * c);
//Check different cases for the discriminant
if(discriminant > 0)
{
root1 = (-b + sqrt(discriminant)) / (2*a);
root2 = (-b - sqrt(discriminant)) / (2*a);
printf("Two distinct and real roots exists: %.2f and %.2f", root1, root2);
}
else if(discriminant == 0)
{
root1 = root2 = -b / (2 * a);
printf("Two equal and real roots exists: %.2f and %.2f", root1, root2);
}
else if(discriminant < 0)
{
root1 = root2 = -b / (2 * a);
imaginary = sqrt(-discriminant) / (2 * a);
printf("Two distinct complex roots exists: %.2f + i%.2f and %.2f - i%.2f",
root1, imaginary, root2, imaginary);
}
return 0;
}
Output:
Enter value of a of quadratic equation (aX^2 + bX + c): 2
Enter value of b of quadratic equation (aX^2 + bX + c): 7
Enter values of c of quadratic equation (aX^2 + bX + c): 2
Two distinct and real roots exist: -0.31 and -3.19
C program to find the roots of a quadratic equation using a function:
#include <stdio.h>
#include <math.h>
void printQuadraticRoots(float a, float b,float c)
{
float root1, root2, imaginary;
float discriminant;
// Find discriminant of the equation
discriminant = (b * b) - (4 * a * c);
//Check different cases for the discriminant
if(discriminant > 0)
{
root1 = (-b + sqrt(discriminant)) / (2*a);
root2 = (-b - sqrt(discriminant)) / (2*a);
printf("Two distinct and real roots exists: %.2f and %.2f", root1, root2);
}
else if(discriminant == 0)
{
root1 = root2 = -b / (2 * a);
printf("Two equal and real roots exists: %.2f and %.2f", root1, root2);
}
else if(discriminant < 0)
{
root1 = root2 = -b / (2 * a);
imaginary = sqrt(-discriminant) / (2 * a);
printf("Two distinct complex roots exists: %.2f + i%.2f and %.2f - i%.2f",
root1, imaginary, root2, imaginary);
}
}
int main()
{
float a, b, c;
printf("Enter value of 'a' of quadratic equation (aX^2 + bX + c): ");
scanf("%f", &a);
printf("Enter value of 'b' of quadratic equation (aX^2 + bX + c): ");
scanf("%f",&b);
printf("Enter values of 'c' of quadratic equation (aX^2 + bX + c): ");
scanf("%f",&c);
printQuadraticRoots(a,b,c);
return 0;
}
Output:
Enter value of ‘a’ of quadratic equation (aX^2 + bX + c): 5
Enter value of ‘b’ of quadratic equation (aX^2 + bX + c): 2
Enter values of ‘c’ of quadratic equation (aX^2 + bX + c): 2
Two distinct complex roots exists: -0.20 + i0.60 and -0.20 – i0.60