This program computes roots of a quadratic equation when its coefficients are known.

The standard form of a quadratic equation is:

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

To find the roots of such equation, we use the formula,

(root1,root2) = (-b ± √b^{2}-4ac)/2

The term `b`

is known as the ^{2}-4ac**discriminant** of a quadratic equation. It tells the nature of the roots.

- If the discriminant is greater than
**0**, the roots are**real**and**different**. - If the discriminant is equal to
**0**, the roots are**real**and**equal**. - If the discriminant is less than
**0**, the roots are**complex**and**different**.

## Example: Roots of a Quadratic Equation

```
// program to solve quadratic equation
let root1, root2;
// take input from the user
let a = prompt("Enter the first number: ");
let b = prompt("Enter the second number: ");
let c = prompt("Enter the third number: ");
// calculate discriminant
let discriminant = b * b - 4 * a * c;
// condition for real and different roots
if (discriminant > 0) {
root1 = (-b + Math.sqrt(discriminant)) / (2 * a);
root2 = (-b - Math.sqrt(discriminant)) / (2 * a);
// result
console.log(`The roots of quadratic equation are ${root1} and ${root2}`);
}
// condition for real and equal roots
else if (discriminant == 0) {
root1 = root2 = -b / (2 * a);
// result
console.log(`The roots of quadratic equation are ${root1} and ${root2}`);
}
// if roots are not real
else {
let realPart = (-b / (2 * a)).toFixed(2);
let imagPart = (Math.sqrt(-discriminant) / (2 * a)).toFixed(2);
// result
console.log(
`The roots of quadratic equation are ${realPart} + ${imagPart}i and ${realPart} - ${imagPart}i`
);
}
```

**Output 1**

Enter the first number: 1 Enter the second number: 6 Enter the third number: 5 The roots of quadratic equation are -1 and -5

The above input values satisfy the first `if`

condition. Here, the discriminant will be greater than **0** and the corresponding code is executed.

**Output 2**

Enter the first number: 1 Enter the second number: -6 Enter the third number: 9 The roots of quadratic equation are 3 and 3

The above input values satisfy the `else if`

condition. Here, the discriminant will be equal to **0** and the corresponding code is executed.

**Output 3**

Enter the first number: 1 Enter the second number: -3 Enter the third number: 10 The roots of quadratic equation are 1.50 + 2.78i and 1.50 - 2.78i

In the above output, the discriminant will be less than **0** and the corresponding code is executed.

In the above program, the `Math.sqrt()`

method is used to find the square root of a number. You can see that `toFixed(2)`

is also used in the program. This rounds up the decimal number to two decimal values.

The above program uses an `if...else`

statements. If you want to learn more about `if...else`

statements, go to JavaScript if...else Statement.