JavaScript Program to Solve Quadratic Equation

In this article, we are going to solve Quadratic equations with the help of JavaScript, A quadratic equation is a polynomial equation of degree 2, represented as ax² + bx + c = 0.

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

A quadratic equation’s zeros, also known as roots, are the values of x that satisfy the equation when substituted, resulting in the left-hand side being equal to zero.

Roots of Quadratic Equation using Sridharacharya Formula

The roots could be found using the below formula (It is known as the formula of Sridharacharya)

The values of the roots depend on the term (b² – 4ac) which is known as the discriminant (D). 

If D > 0:
        => This occurs when b2 > 4ac.
        => The roots are real and unequal.
        => The roots are {-b + √(b2 – 4ac)}/2a and {-b – √(b2 – 4ac)}/2a.
If D = 0:
        => This occurs when b2 = 4ac.
        => The roots are real and equal.
        => The roots are (-b/2a).
If D < 0:
        => This occurs when b2 < 4ac.
        => The roots are imaginary and unequal.
        => The discriminant can be written as (-1 * -D).
        => As D is negative, -D will be positive.
        => The roots are {-b ± √(-1*-D)} / 2a = {-b ± i√(-D)} / 2a = {-b ± i√-(b2 – 4ac)}/2a where i = √-1.

JavaScript Program to Solve Quadratic Equation using Sridharacharya Formula

Using the Sridharacharya formula to solve a quadratic equation with coefficients a, b, and c, finding the roots with positive or negative square roots of the discriminant.

Example: In this example, we are using the above-explained approach.

Javascript

// JavaScript program to find roots
// of a quadratic equation

// Prints roots of quadratic
// equation ax * 2 + bx + x
function findRoots(a, b, c) {

    // If a is 0, then equation is not
    // quadratic, but linear
    if (a == 0) {
        console.log("Invalid");
        return;
    }

    let d = b * b - 4 * a * c;
    let sqrt_val = Math.sqrt(Math.abs(d));

    if (d > 0) {
        console.log('Roots are real and different');

        console.log(
            (-b + sqrt_val) / (2 * a) + " and " +
            (-b - sqrt_val) / (2 * a)
        );
    }
    else if (d == 0) {
        console.log('Roots are real and same');

        console.log(-b / (2 * a) + " and " +
            -b / (2 * a));
    }

    // d < 0
    else {
        console.log('Roots are complex');

        console.log(-b / (2 * a) + " + i" +
            sqrt_val / (2 * a) + " and " +
            -b / (2 * a) + " - i" + sqrt_val) / (2 * a);
    }
}

// Driver Code
let a = 1, b = -7, c = 12;

// Function call
findRoots(a, b, c);

Output

Roots are real and different
4 and 3

JavaScript Program to Solve Quadratic Equation using the Custom function

In this approach, we create a custom function to calculate the roots without explicitly using the quadratic formula.

Example: In this example, The myResult(a, b, c) function calculates the discriminant of a quadratic equation with coefficients a, b, and c. Based on the discriminant, it finds the real or repeated roots

Javascript

function findRoots(a, b, c) {
    return b * b - 4 * a * c;
}

function myResult(a, b, c) {
    const d = findRoots(a, b, c);

    if (d > 0) {
        const root1 = (-b + Math.sqrt(d)) / (2 * a);
        const root2 = (-b - Math.sqrt(d)) / (2 * a);
        return [root1, root2];
    } else if (d === 0) {
        const root = -b / (2 * a);
        return [root];
    } else {
        return [];
    }
}

// Example usage:
let a = 1;
let b = -3;
let c = 2;
let result = myResult(a, b, c);
console.log("Roots:", result);

Output

Roots: [ 2, 1 ]