To Calculate Roots of A Quadratic Equation in Java

Introduction

A quadratic equation is a second-degree polynomial equation in the form:

where a, b, and c are coefficients, and x represents the variable. The roots of the equation are the values of x that satisfy the equation. There are three possible cases for the roots:

• Two distinct real roots
• One real root (a repeated root)
• No real roots (complex roots)

In this guide, we'll explore how to calculate these roots using Java programming.

Quadratic Equation Formula

The roots of a quadratic equation can be found using the quadratic formula:

Where:

• a, b, c are the coefficients of the quadratic equation
• √(b² - 4ac) is the discriminant
• The discriminant determines the nature of the roots:

Java Implementation

Here's a Java method to calculate the roots of a quadratic equation:

public class QuadraticEquation {
    public static void calculateRoots(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("Two distinct real roots:");
            System.out.println("Root 1: " + root1);
            System.out.println("Root 2: " + root2);
        } else if (discriminant == 0) {
            double root = -b / (2 * a);
            System.out.println("One real root (repeated):");
            System.out.println("Root: " + root);
        } else {
            double realPart = -b / (2 * a);
            double imaginaryPart = Math.sqrt(-discriminant) / (2 * a);
            System.out.println("No real roots (complex roots):");
            System.out.println("Root 1: " + realPart + " + " + imaginaryPart + "i");
            System.out.println("Root 2: " + realPart + " - " + imaginaryPart + "i");
        }
    }
}

This implementation:

• Calculates the discriminant first
• Checks the discriminant value to determine the nature of roots
• Provides appropriate output for each case
• Handles complex roots when necessary

Worked Example

Let's calculate the roots of the equation 2x² + 4x - 6 = 0.

Step 1: Calculate the discriminant

Since the discriminant is positive (64 > 0), there are two distinct real roots.

Step 2: Calculate the roots

The roots of the equation are x = 1 and x = -3.