The standard form of a quadratic equation is:

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

Here, `a`, `b`, and `c` are real numbers and `a` can't be equal to 0.

We can calculate the root of a quadratic by using the formula:

`x = (-b ± √(b`^{2}-4ac)) / (2a)

The `±`

sign indicates that there will be two roots:

`root1 = (-b + √(b`^{2}-4ac)) / (2a)
root1 = (-b - √(b^{2}-4ac)) / (2a)

The term `b`

is known as the ^{2}-4ac**determinant** of a quadratic equation. It specifies the nature of roots. That is,

- if
**determinant > 0**, roots are real and different - if
**determinant == 0**, roots are real and equal - if
**determinant < 0**, roots are complex complex and different

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

```
public class Main {
public static void main(String[] args) {
// value a, b, and c
double a = 2.3, b = 4, c = 5.6;
double root1, root2;
// calculate the determinant (b
```^{2} - 4ac)
double determinant = b * b - 4 * a * c;
// check if determinant is greater than 0
if (determinant > 0) {
// two real and distinct roots
root1 = (-b + Math.sqrt(determinant)) / (2 * a);
root2 = (-b - Math.sqrt(determinant)) / (2 * a);
System.out.format("root1 = %.2f and root2 = %.2f", root1, root2);
}
// check if determinant is equal to 0
else if (determinant == 0) {
// two real and equal roots
// determinant is equal to 0
// so -b + 0 == -b
root1 = root2 = -b / (2 * a);
System.out.format("root1 = root2 = %.2f;", root1);
}
// if determinant is less than zero
else {
// roots are complex number and distinct
double real = -b / (2 * a);
double imaginary = Math.sqrt(-determinant) / (2 * a);
System.out.format("root1 = %.2f+%.2fi", real, imaginary);
System.out.format("\nroot2 = %.2f-%.2fi", real, imaginary);
}
}
}

**Output**

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 the 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.

We have used the `format()`

method to print the calculated roots.

The `format()`

function can also be replaced by `printf()`

as:

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