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: Kotlin Program to Find Roots of a Quadratic Equation

```
fun main(args: Array<String>) {
val a = 2.3
val b = 4
val c = 5.6
val root1: Double
val root2: Double
val output: String
val determinant = b * b - 4.0 * 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)
output = "root1 = %.2f and root2 = %.2f".format(root1, root2)
}
// Condition for real and equal roots
else if (determinant == 0.0) {
root2 = -b / (2 * a)
root1 = root2
output = "root1 = root2 = %.2f;".format(root1)
}
// If roots are not real
else {
val realPart = -b / (2 * a)
val imaginaryPart = Math.sqrt(-determinant) / (2 * a)
output = "root1 = %.2f+%.2fi and root2 = %.2f-%.2fi".format(realPart, imaginaryPart, realPart, imaginaryPart)
}
println(output)
}
```

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 output to be printed is then stored in a string variable `output` using the Kotlin's standard libary function `format()`

. The output is then printed using `println()`

.

Here's the equivalent Java code of the above program: Java Program to Find all Roots of a Quadractic Equation