The standard form of a quadratic equation is:

ax^{2}+ bx + c = 0, where a, b and c are real numbers and a ≠ 0

The term `b`

is known as the determinant of a quadratic equation. The determinant tells the nature of the roots.^{2}-4ac

- 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 `b`

.^{2} - 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);