Java program to find the roots of a quadratic equation

Java program to find the roots of a quadratic equation:

In this post, we will learn how to find the roots of a quadratic equation in Java. We will take the values as inputs from the user and print the root values.

How to find the roots of a quadratic equation:

Below is the formula of a quadratic equation:

ax^2 + bx + c = 0

Here, a, b and c are all real numbers and a can’t be equal to 0. We can use the below formula to find the roots of this quadratic equation:

-b ± √(b^2-4ac)/ 2a

There will be two roots. The ± sign is used for that.

Also, the value under the square root, b2-4ac is called the discriminant. Based on the value of this discriminant, the roots of a quadratic equation is defined.

If it is equal to 0, roots are equal and both are real numbers.
If it is greater than 0, roots are different and both are real numbers.
If it is less than 0, roots are different and both are complex numbers.

Java program:

We will take the values of a, b and c as inputs from the user and print the roots for that quadratic equation.

import java.util.Scanner;

class Main {

    public static void main(String[] args) {
        double a, b, c, d;
        double firstRoot, secondRoot;

        Scanner sc = new Scanner(System.in);

        System.out.println("Enter the values of a, b and c: ");
        a = sc.nextDouble();
        b = sc.nextDouble();
        c = sc.nextDouble();

        d = b * b - 4 * a * c;

        if (d == 0) {
            firstRoot = secondRoot = -b / (2 * a);
            System.out.format("First root: %.2f, second root: %.2f", firstRoot, secondRoot);
        } else if (d > 0) {
            firstRoot = -b + Math.sqrt(d) / 2 * a;
            secondRoot = -b - Math.sqrt(d) / 2 * a;

            System.out.format("First root: %.2f, second root: %.2f", firstRoot, secondRoot);
        } else {
            double r = -b / (2 * a);
            double i = Math.sqrt(-d) / (2 * a);

            System.out.format("First root: %.2f+%.2fi\n", r, i);
            System.out.format("Second root: %.2f-%.2fi", r, i);

        }

    }
}

Here,

a, b, c variables are to hold the a, b, and c values of the quadratic equation.
d is to hold the discriminant.
We are taking the values of a, b, and c from user and it finds the values of d by using the above formula.
Based on the value of d, it finds the roots of the quadratic equation.
The if block will run if the value of d is equal to 0.
The else if will run if it is greater than 0.
The else block will run if it is less than 0.
- Inside the blocks, we are finding the roots by using the same formula we seen above. We are using System.out.format to print the values of the roots.

Sample output:

If you run this program, it will give output as like below:

Enter the values of a, b and c: 
3
4
5
First root: -0.67+1.11i
Second root: -0.67-1.11i

Enter the values of a, b and c: 
1
20
2
First root: -10.10, second root: -29.90

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Java program to find the roots of a quadratic equation