**Java Programs**

➤ Check Even Number

➤ Check Odd Number

➤ Java Even-Odd

➤ Greatest of 3 numbers

➤ Exponents in Java

➤ Java Leap Year Program

➤ Display Multiplication Table

➤ Reverse of a number

➤ Factors of a Number

➤ Java LCM of 2 Numbers

➤ Java HCF of 2 Numbers

➤ Quadratic Equation Program

➤ Square Root of Number

➤ Perfect Square Program

➤ Simple Calculator Program

➤ BMI Calculator Java

➤ Factorial of a Number

➤ Factorial Using Recursion

**#**Java Programs to Find Sum

**#**Java Conversion Programs

**#**Java Program on Series

**#**Java Pattern Programs

**#**Java Number Programs

**Java Array Programs**

**Java String Programs**

In this post, we will develop a Java program for the quadratic equation. It will find the roots of the given quadratic equation.

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form of the quadratic equation is ax² + bx + c = 0 where a, b and c are real and a !=0, x is an unknown variable. The nature of roots is determined by the discriminant.

**Quadratic formula Java**

The discriminant of the Quadratic equation is calculated as b²-4*a*c.

`discriminant(d) = b² - 4*a*c`

The nature of the roots are given as,

=> If discriminant>1 then the roots are real and different`=>`

If discriminant=0 then the roots are real and equal

=> discriminant<1 then the roots are complex and different

For the quadratic equation ax² + bx + c = 0, if we denote the discriminant as d, then their roots

If d>1 then the roots are real and different

root1 = (-b + √d)/2a

root2 = (-b – √d)/2a

If d=0 then both roots are -b/2a

If d<1 then roots are complex and different

root1 = -b/2a + i (√d/2a)

root2 = -b/2a – i (√d/2a)

## Java program to find roots of Quadratic Equation

```
import java.util.Scanner;
public class QuadraticProgram {
public static void main(String[] args) {
// declare variables
int a, b, c;
int desc ;
int root1, root2 ;
int realPart, imaginaryPart;
// create Scanner class object
// to read inputs
Scanner scan = new Scanner(System.in);
// read inputs
System.out.print("Enter coefficients "
+ "(a, b, and c values): ");
a = scan.nextInt();
b = scan.nextInt();
c = scan.nextInt();
// display Quadratic equation
System.out.print("The quadratic equation: ");
System.out.format("%d*x^2 + %d*x + %d = 0\n",
a, b, c);
// calculate discriminant
desc = (b*b) - (4*a*c);
// find roots
if(desc > 1) {
// both roots are real and different
root1=(-b+(int)Math.sqrt(desc))/2*a;
root2=(-b-(int)Math.sqrt(desc))/2*a;
// display roots
System.out.println("Roots are = "+
root1 + ", "+ root2);
}
else if(desc == 0) {
// both roots are real and equal
root1=(-b+(int)Math.sqrt(desc))/2*a;
root2 = root1;
// display roots
System.out.println("Roots are = "+
root1+ ", "+ root2);
}
else {
// roots are complex and different
realPart = -b/(2*a);
imaginaryPart=(int)Math.sqrt(desc)/(2*a);
System.out.format("root1 = %d + i(%d)\n",
realPart, imaginaryPart);
System.out.format("root2 = %d - i(%d)\n",
realPart, imaginaryPart);
}
// close Scanner class object
scan.close();
}
}
```

The output for the different test cases are:-

Enter coefficients (a, b, and c values): 1 -1 -6

The quadratic equation: 1*x^2 + -1*x + -6 = 0

Roots are = 3, -2

Enter coefficients (a, b, and c values): 1 0 -25

The quadratic equation: 1*x^2 + 0*x + -25 = 0

Roots are = 5, -5

Enter coefficients (a, b, and c values): 1 -12 36

The quadratic equation: 1*x^2 + -12*x + 36 = 0

Roots are = 6, 6

Enter coefficients (a, b, and c values): 1 4 5

The quadratic equation: 1*x^2 + 4*x + 5 = 0

root1 = -2 + i(0)

root2 = -2 – i(0)

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