RootFinder.js

RootFinder.js is a lightweight JavaScript library for finding the roots of quadratic equations and cubic equations. It leverages the Complex.js library to handle complex solutions, ensuring precision and correctness when dealing with both real and complex numbers.

Features

• Solve quadratic equations of the form ax² + bx + c = 0.
• Solve cubic equations of the form ax³ + bx² + cx + d = 0 using Cardano's method.
• Support for complex roots using Complex.js.

Installation

You can install RootFinder.js via npm:

npm install @rawify/rootfinder

Or with yarn:

yarn add @rawify/rootfinder

Alternatively, download or clone the repository:

git clone https://github.com/rawify/RootFinder.js

Usage

Include the rootfinder.min.js file in your project:

<script src="path/to/rootfinder.min.js"></script>
<script src="path/to/complex.min.js"></script>
<script>
  const roots = RootFinder.quadratic(2, 5, 6);
  ...
</script>

Or in a Node.js project:

const RootFinder = require('@rawify/rootfinder');

or

import RootFinder from '@rawify/rootfinder';

Solving Quadratic Equations

To find the roots of a quadratic equation ax² + bx + c = 0:

const roots = RootFinder.quadratic(1, -3, 2);
console.log(roots); // Output: [ Complex { re: 2 }, Complex { re: 1 } ]

If the equation has complex roots:

const complexRoots = RootFinder.quadratic(1, 0, 1);
console.log(complexRoots); // Output: [ Complex { re: 0, im: 1 }, Complex { re: 0, im: -1 } ]

Solving Cubic Equations

To find the roots of a cubic equation ax³ + bx² + cx + d = 0:

const roots = RootFinder.cubic(1, -6, 11, -6);
console.log(roots); // Output: [ Complex { re: 1 }, Complex { re: 2 }, Complex { re: 3 } ]

For cubic equations with complex roots:

const complexRoots = RootFinder.cubic(1, 0, 0, -1);
console.log(complexRoots); // Output: [ Complex { re: 1, im: 0 }, Complex { re: -0.5, im: 0.866 }, Complex { re: -0.5, im: -0.866 } ]

API

quadratic(a, b, c[, returnReal=false])

Solves the quadratic equation ax² + bx + c = 0.

• Parameters:

  • a (Number): Coefficient of x²
  • b (Number): Coefficient of x
  • c (Number): Constant term
  • returnReal (optional Boolean): Decide if only real roots should be returned

• Returns: An array of roots, which can contain real or complex numbers.

cubic(a, b, c, d[, returnReal=false])

Solves the cubic equation ax³ + bx² + cx + d = 0 using Cardano's method.

• Parameters:

  • a (Number): Coefficient of x³
  • b (Number): Coefficient of x²
  • c (Number): Coefficient of x
  • d (Number): Constant term
  • returnReal (optional Boolean): Decide if only real roots should be returned

• Returns: An array of roots, which can contain real or complex numbers.

Coding Style

As every library I publish, RootFinder.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.

Building the library

After cloning the Git repository run:

npm install
npm run build

Run a test

Testing the source against the shipped test suite is as easy as

npm run test

Copyright and Licensing

Copyright (c) 2025, Robert Eisele Licensed under the MIT license.