# Java Program to Find all Roots of a Quadratic Equation

In this program, you'll learn to find all roots of a quadratic equation and print them using format() in Java.

The standard form of a quadratic equation is:

```ax2 + bx + c = 0, where
a, b and c are real numbers and
a ≠ 0
```

The term `b2-4ac` is known as the determinant of a quadratic equation. The determinant tells the nature of the roots.

• If determinant is greater than 0, the roots are real and different.
• If determinant is equal to 0, the roots are real and equal.
• If determinant is less than 0, the roots are complex and different.

## Example: Java Program to Find Roots of a Quadratic Equation

``````public class Quadratic {

public static void main(String[] args) {

double a = 2.3, b = 4, c = 5.6;
double root1, root2;

double determinant = b * b - 4 * a * c;

// condition for real and different roots
if(determinant > 0) {
root1 = (-b + Math.sqrt(determinant)) / (2 * a);
root2 = (-b - Math.sqrt(determinant)) / (2 * a);

System.out.format("root1 = %.2f and root2 = %.2f", root1 , root2);
}
// Condition for real and equal roots
else if(determinant == 0) {
root1 = root2 = -b / (2 * a);

System.out.format("root1 = root2 = %.2f;", root1);
}
// If roots are not real
else {
double realPart = -b / (2 *a);
double imaginaryPart = Math.sqrt(-determinant) / (2 * a);

System.out.format("root1 = %.2f+%.2fi and root2 = %.2f-%.2fi", realPart, imaginaryPart, realPart, imaginaryPart);
}
}
}``````

When you run the program, the output will be:

`root1 = -0.87+1.30i and root2 = -0.87-1.30i`

In the above program, the coefficients a, b and c are set to 2.3, 4 and 5.6 respectively. Then, the `determinant` is calculated as `b2 - 4ac`.

Based on the value of determinant, the roots are calculated as given in the formula above. Notice we've used library function Math.sqrt() to calculate the square root of a number.

The calculated roots (either real or complex) are printed on the screen using `format()` function in Java. The `format()` function can also be replaced by `printf()` as:

`System.out.printf("root1 = root2 = %.2f;", root1);`