C Program to Find Roots of Quadratic Equation

This article will deeply discuss how to find the root of a quadratic equation using C. Finding roots of a quadratic equation will help in building the logic which will enhance your coding career. Let’s discuss and understand what a quadratic equation is and we will see the C program to find roots of quadratic equation.
Firstly, let’s look and see what a quadratic equation is?

What is a quadratic equation?

A quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2.
The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a can’t be 0. Example of quadratic equation: 3x^2 + 3x + 1.
Let’s discuss what roots of a quadratic equation are and how to get the roots from the equation….

The term b^2 – 4ac is called the discriminant of a quadratic equation. It tells the nature of the roots.

If the discriminant is greater than 0, the roots are real and different.
If the discriminant is equal to 0, the roots are real and equal.
If the discriminant is less than 0, the roots are complex and different.

Algorithm to Find Roots of Quadratic Equation

  1. Input the value of a, b, c.
  2. Calculate k = bb – 4a*c
  3. If (d < 0)
    • Print "Roots are Imaginary, calculate root1 = (-b +i ?k)/ 2a and root2 =(b + i?k)/ 2a.
  4. else if (d = 0)
    • Print "Roots are Equal" and calculate root1 = root2 = (-b / 2*a)
  5. else
    • Print "Roots are real and calculate root1 = -b + ?d / 2a and root2 = -b – ?d / 2a.
  6. Print root1 and root2.
  7. End the algorithm.

Code Implementation to Find Roots of Quadratic Equation

#include <math.h>
#include <stdio.h>
int main() {
    double a, b, c, discriminant, root1, root2, realPart, imagPart;
    printf("Enter coefficients a, b and c: ");
    scanf("%lf %lf %lf", &a, &b, &c);
    discriminant = b * b - 4 * a * c;
    if (discriminant > 0) {
        root1 = (-b + sqrt(discriminant)) / (2 * a);
        root2 = (-b - sqrt(discriminant)) / (2 * a);
        printf("root1 = %.2lf and root2 = %.2lf", root1, root2);
    }
    else if (discriminant == 0) {
        root1 = root2 = -b / (2 * a);
        printf("root1 = root2 = %.2lf;", root1);
    }
    else {
        realPart = -b / (2 * a);
        imagPart = sqrt(-discriminant) / (2 * a);
        printf("root1 = %.2lf+%.2lfi and root2 = %.2f-%.2fi", realPart, imagPart, realPart, imagPart);
    }
    return 0;
} 
Output
root1 = -1.00+1.41i and root2 = -1.00-1.41i

Time Complexity

O(1) will be the time complexity as general mathematics is used to find the roots of the quadratic equation.

Conclusion

This blog gives the best explanation to find the roots of the quadratic equation in c. Regularly solving problems like finding roots of the quadratic equation will boost your career in the programming field. Don’t stop here, try more logical questions like finding roots of the quadratic equation, which not only build your logics but also by practicing them your programming skills will also boosten up.

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