Program to Find Roots of a Quadratic Equation in Java

Finding Roots of a Quadratic Equation

A quadratic equation is in the form ax² + bx + c = 0. The roots of this equation can be real or complex depending on the discriminant (D = b² - 4ac).

We will explore three different methods to find the roots of a quadratic equation in Java.

Method 1: Using the Quadratic Formula

This method uses the quadratic formula: x = (-b ± sqrt(b² - 4ac)) / (2a).

import java.util.Scanner;

public class QuadraticEquation {
    public static void findRoots(double a, double b, double c) {
        double discriminant = b * b - 4 * a * c;
        if (discriminant > 0) {
            double root1 = (-b + Math.sqrt(discriminant)) / (2 * a);
            double root2 = (-b - Math.sqrt(discriminant)) / (2 * a);
            System.out.println("Real and Distinct Roots: " + root1 + ", " + root2);
        } else if (discriminant == 0) {
            double root = -b / (2 * a);
            System.out.println("Real and Equal Root: " + root);
        } else {
            double realPart = -b / (2 * a);
            double imagPart = Math.sqrt(-discriminant) / (2 * a);
            System.out.println("Complex Roots: " + realPart + " + " + imagPart + "i, " + realPart + " - " + imagPart + "i");
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter coefficients a, b, and c: ");
        double a = scanner.nextDouble();
        double b = scanner.nextDouble();
        double c = scanner.nextDouble();
        findRoots(a, b, c);
        scanner.close();
    }
}
            

Method 2: Using Factorization

Factorization is an alternative method where we break the middle term to find the roots.

import java.util.Scanner;

public class QuadraticFactorization {
    public static void factorize(int a, int b, int c) {
        boolean found = false;
        for (int i = -100; i <= 100; i++) {
            for (int j = -100; j <= 100; j++) {
                if (i * j == a * c && i + j == b) {
                    System.out.println("Roots are: " + (-j) + "/" + a + " and " + (-i) + "/" + a);
                    found = true;
                    return;
                }
            }
        }
        if (!found) {
            System.out.println("Cannot be factorized easily.");
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter coefficients a, b, and c: ");
        int a = scanner.nextInt();
        int b = scanner.nextInt();
        int c = scanner.nextInt();
        factorize(a, b, c);
        scanner.close();
    }
}
            

Method 3: Using Recursion

This method recursively calculates the discriminant and finds the roots.

import java.util.Scanner;

public class QuadraticRecursion {
    public static void findRootsRecursive(double a, double b, double c, double d) {
        if (d > 0) {
            double root1 = (-b + Math.sqrt(d)) / (2 * a);
            double root2 = (-b - Math.sqrt(d)) / (2 * a);
            System.out.println("Real and Distinct Roots: " + root1 + ", " + root2);
        } else if (d == 0) {
            double root = -b / (2 * a);
            System.out.println("Real and Equal Root: " + root);
        } else {
            double realPart = -b / (2 * a);
            double imagPart = Math.sqrt(-d) / (2 * a);
            System.out.println("Complex Roots: " + realPart + " + " + imagPart + "i, " + realPart + " - " + imagPart + "i");
        }
    }

    public static void calculateDiscriminant(double a, double b, double c) {
        double d = b * b - 4 * a * c;
        findRootsRecursive(a, b, c, d);
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter coefficients a, b, and c: ");
        double a = scanner.nextDouble();
        double b = scanner.nextDouble();
        double c = scanner.nextDouble();
        calculateDiscriminant(a, b, c);
        scanner.close();
    }
}