Lesson 18. Solving Quadratic Equations with Java | Learn Java for Beginners

What is a Quadratic Equation?

A quadratic equation is one of the basic types of mathematical equations that you commonly encounter. The equation is in the following form:

ax^2 + bx + c = 0

Where a, b, and c are constants, and x is the variable. The goal is to find the value of x that satisfies this equation.

When solving a quadratic equation, we use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where:

• b^2 - 4ac is called the delta or the discriminant of the quadratic equation.
• Based on the value of delta, we determine the number of solutions for the equation.

Cases of a Quadratic Equation

1. If delta > 0: The equation has two distinct solutions.
2. If delta = 0: The equation has one repeated solution.
3. If delta < 0: The equation has no real solutions.

Writing a Program to Solve a Quadratic Equation in Java

In this lesson, we will write a Java program to solve a quadratic equation. This program will ask the user to input the values for a, b, and c, then calculate and display the solution(s) if they exist. The steps are as follows:

• Step 1: Declare Variables and Input Data: We will need three variables a, b, and c to store the coefficients of the equation. Additionally, we will need a variable to store the value of delta (discriminant).
• Step 2: Calculate delta and Solutions: Use the formula above to calculate the value of delta. Based on the value of delta, we will determine the number of solutions and calculate the solutions of the equation.
• Step 3: Display the Results: After the calculations, we will print the results to the screen, displaying the solution(s) of the equation.

From these steps, we proceed to write the code for the program as follows:

import java.util.Scanner;

public class SolveQuadraticEquation {

    public static void main(String[] args) {
        // Initialize Scanner object to receive user input
        Scanner scanner = new Scanner(System.in);

        // Input the coefficients of the quadratic equation
        System.out.print("Enter coefficient a: ");
        double a = scanner.nextDouble();

        System.out.print("Enter coefficient b: ");
        double b = scanner.nextDouble();

        System.out.print("Enter coefficient c: ");
        double c = scanner.nextDouble();

        // Calculate delta
        double delta = b * b - 4 * a * c;

        // Handle cases based on the value of delta
        if (a == 0) {
            System.out.println("This is not a quadratic equation.");
        } else if (delta > 0) {
            // If delta > 0, the equation has two distinct solutions
            double x1 = (-b + Math.sqrt(delta)) / (2 * a);
            double x2 = (-b - Math.sqrt(delta)) / (2 * a);
            System.out.println("The equation has two distinct solutions:");
            System.out.println("Solution x1 = " + x1);
            System.out.println("Solution x2 = " + x2);
        } else if (delta == 0) {
            // If delta = 0, the equation has one repeated solution
            double x = -b / (2 * a);
            System.out.println("The equation has one repeated solution: x = " + x);
        } else {
            // If delta < 0, the equation has no real solutions
            System.out.println("The equation has no real solutions.");
        }

        // Close the scanner object
        scanner.close();
    }
}

Code Explanation

1. Input Data: We use Scanner to get the coefficients a, b, and c from the user.
2. Calculate delta: The delta variable is calculated using the formula b^2 - 4ac.
3. Handle the Cases:
   • If a = 0, it's not a quadratic equation.
   • If delta > 0, the program calculates two distinct solutions.
   • If delta = 0, the program calculates one repeated solution.
   • If delta < 0, the program outputs that the equation has no real solutions.

Running the Program and Checking Results

Example 1: Equation with Two Distinct Solutions

Input:

• a = 1
• b = -5
• c = 6

The program will calculate delta = 1 and output:

The equation has two distinct solutions:
Solution x1 = 3.0
Solution x2 = 2.0

Example 2: Equation with One Repeated Solution

Input:

• a = 1
• b = -4
• c = 4

The program will calculate delta = 0 and output:

The equation has one repeated solution: x = 2.0

Example 3: Equation with No Real Solutions

Input:

• a = 1
• b = 2
• c = 5

The program will calculate delta = -16 and output:

The equation has no real solutions.

Conclusion

Solving quadratic equations in Java is a basic but important exercise that helps you understand how to use conditional statements (if-else) and mathematical formulas in programming. The program above not only solves a mathematical problem but also helps you practice fundamental Java programming skills.

If you want to experiment further, you can extend this program to support solving quadratic equations with coefficients input from a file, or add a graphical user interface (GUI) to make the program more user-friendly.

Next lesson: Lesson 19. Switch ... Case Statements in Java