# Java program to find the roots of a quadratic equation

Roots of a quadratic equation are determined by the following formula:

$$x = \frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$$

To calculate the roots −

• Calculate the determinant value (b*b)-(4*a*c).
• If determinant is greater than 0 roots are [-b +squareroot(determinant)]/2*a and [-b -squareroot(determinant)]/2*a.
• If determinant is equal to 0 root value is (-b+Math.sqrt(d))/(2*a)

## Example

import java.util.Scanner;
public static void main(String args[]){
double secondRoot = 0, firstRoot = 0;
Scanner sc = new Scanner(System.in);
System.out.println("Enter the value of a ::");
double a = sc.nextDouble();

System.out.println("Enter the value of b ::");
double b = sc.nextDouble();

System.out.println("Enter the value of c ::");
double c = sc.nextDouble();

double determinant = (b*b)-(4*a*c);
double sqrt = Math.sqrt(determinant);

if(determinant>0){
firstRoot = (-b + sqrt)/(2*a);
secondRoot = (-b - sqrt)/(2*a);
System.out.println("Roots are :: "+ firstRoot +" and "+secondRoot);
}else if(determinant == 0){
System.out.println("Root is :: "+(-b + sqrt)/(2*a));
}
}
}

## Output

Enter the value of a ::
15
Enter the value of b ::
68
Enter the value of c ::
3
Roots are :: -0.044555558333472335 and -4.488777774999861