In algebra, a **quadratic equation** (from Latin * quadratus* ‘square‘) is any equation that can be rearranged in standard form as:

*ax*^{2} + *bx* + *c* = 0

This java program will try to find the roots of this **quadratic equation** based on the parameters **a**, **b** and **c**. This parameters are required to be given as input from the console and then the program show if there is root(s) (solutions) **x1** and **x2** for this equation.

There are three cases based on the values of the Discriminant (b** ^{2}**-4ac):

- Positive Discriminant -> There are two roots
**x1**and**x2**which are solution of the given equation - Discriminant is equal to Zero -> There is only one root
**x1**which is solution of the given equation - Negative Discriminant -> Then there are no real roots. Rather, there are two distinct (non-real) complex roots

More information about Quadratic equation

import java.util.Scanner; public class QuadraticEquation { public static void main(String[] args) { // ax^2 + bx + c = 0 int a, b, c; try(Scanner in = new Scanner(System.in)) { System.out.println("Please give integer for a, b, and c: "); a = in.nextInt(); b = in.nextInt(); c = in.nextInt(); } System.out.println("Now the program will try to find x roots "); System.out.println("For the Quadratic equation: "); System.out.format("%d*x^2+%d*x+%d=0", a, b, c ); System.out.println(); // Discriminant // b^2-4ac double d = Math.pow(b, 2) - 4*a*c; // find roots if(d > 1) { // Final find of distinct roots // x1 = (-b+√D)/2a x2 = (-b-√D)/2a double x1 = (-b + Math.sqrt(d))/2*a; double x2 = (-b - Math.sqrt(d))/2*a; System.out.println("x1: " + x1); System.out.println("x2: " + x2); } else if(d == 0) { // both roots are real and equal double x1 = (-b + Math.sqrt(d))/2*a; System.out.println("Root is = "+ x1); } else { // roots are complex. They have real and imaginary part double real = -b / (2*a); double imaginary = Math.sqrt(-d) / (2*a); System.out.format("x1 = %f + i(%f)\n", real, imaginary); System.out.format("x2 = %f - i(%f)\n", real, imaginary); } } }

Output:

```
1
7
-78
Now the program will try to find x roots
For the Quadratic equation:
1*x^2+7*b+-78=0
x1: 6.0
x2: -13.0
```