Added QuadraticRoots to Math/QuadraticRoots.js (TheAlgorithms#1376)

* Added QuadraticRoots in the Math/QuadraticRoots

* Fixed math/QyadraticRoots var to let

* Added relevant links math/QyadraticRoots

* Added relevant links math/QyadraticRoots and fixed let - const

* Added the changes and @see notation in Math/QuadraticRoots.js

* Added the changes Math/QuadraticRoots.js and return an empty []

* Readd describe block, remove redundant comments

* Changed [1,1] to [1]

---------

Co-authored-by: Dibya <[email protected]>
Co-authored-by: Lars Müller <[email protected]>

Author: 3 people

Maths/QuadraticRoots.js

@@ -0,0 +1,37 @@
+/**
+ * @see https://www.cuemath.com/algebra/roots-of-quadratic-equation/
+ * @author Dibya Debayan Dash
+ * Calculates the roots of a quadratic equation of the form ax^2 + bx + c = 0.
+ *
+ * @param {number} a - Coefficient of x^2.
+ * @param {number} b - Coefficient of x.
+ * @param {number} c - Constant term.
+ * @returns {number[]} - An array containing the roots if they are real,
+ *                      or an empty array indicating no real roots.
+ *
+ * @example
+ * // Find the roots of the quadratic equation: 2x^2 - 4x + 2 = 0
+ * const roots = quadraticRoots(2, -4, 2);
+ * // Expected output: [1]
+ */
+const quadraticRoots = (a, b, c) => {
+  // Calculate the discriminant
+  const discriminant = b * b - 4 * a * c
+
+  // Check if roots are real
+  if (discriminant < 0) {
+    return []
+  } else if (discriminant === 0) {
+    // One real root
+    return [-b / (2 * a)]
+  } else {
+    // Two real roots
+    const sqrtDiscriminant = Math.sqrt(discriminant)
+    return [
+      (-b + sqrtDiscriminant) / (2 * a),
+      (-b - sqrtDiscriminant) / (2 * a)
+    ]
+  }
+}
+
+export { quadraticRoots }

Maths/test/QuadraticRoots.test.js

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+import { quadraticRoots } from '../QuadraticRoots.js'
+
+describe('quadratic roots', () => {
+  it('returns an array with two real roots when the discriminant is positive', () => {
+    expect(quadraticRoots(1, -3, 2)).toEqual([2, 1])
+  })
+  it('returns an array with one real root when the discriminant is zero', () => {
+    expect(quadraticRoots(1, -2, 1)).toEqual([1])
+  })
+  it('returns an empty array indicating no real roots when the discriminant is negative', () => {
+    expect(quadraticRoots(1, 2, 5)).toEqual([])
+  })
+})