Added Polynomial Roots Calculator (#1170)

Rakesh9100 · Jun 5, 2024 · 550be82 · 550be82
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diff --git a/Calculators/Polynomial-Roots-Calculator/README.md b/Calculators/Polynomial-Roots-Calculator/README.md
@@ -0,0 +1,15 @@
+# <p align="center">Polynomial Roots Calculator</p>
+
+## Description :-
+
+This Calculator is used to calculate the real and imaginary roots of a given polynomial more effectively and easily. It is designed to calculate the roots for degrees 2, 3, and 4 of polynomials.
+
+## Tech Stacks :-
+
+- HTML
+- CSS
+- JavaScript
+
+## Screenshots :-
+
+![image](https://github.com/Rakesh9100/CalcDiverse/assets/142529986/054ad35e-88ad-41f2-b235-0d25b7b65bfb)
diff --git a/Calculators/Polynomial-Roots-Calculator/assets/boy.svg b/Calculators/Polynomial-Roots-Calculator/assets/boy.svg
diff --git a/Calculators/Polynomial-Roots-Calculator/index.html b/Calculators/Polynomial-Roots-Calculator/index.html
@@ -0,0 +1,65 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/aos/2.3.4/aos.css">
+    <link rel="stylesheet" href="style.css">
+    <title>Polynomial Roots Calculator</title>
+</head>
+<body>
+    <div class="hero-section">
+        <div class="calculator" >
+            <h1 data-aos="fade-right">Roots Calculator</h1>
+            <div class="input-group" >
+                <label for="degree">Degree of Polynomial:</label>
+                <select id="degree" onchange="showCoefficientInputs()" style="width: 25rem;">
+                    <option value="2">2</option>
+                    <option value="3">3</option>
+                    <option value="4">4</option>
+                </select>
+            </div>
+            <div id="coefficients">
+                <div class="input-group" >
+                    <label for="a">Coefficient a:</label>
+                    <input type="number" id="a" placeholder="e.g., 3">
+                </div>
+                <div class="input-group">
+                    <label for="b">Coefficient b:</label>
+                    <input type="number" id="b" placeholder="e.g., 2">
+                </div>
+                <div class="input-group">
+                    <label for="c">Coefficient c:</label>
+                    <input type="number" id="c" placeholder="e.g., 1">
+                </div>
+                <div class="input-group" id="d-group" style="display: none;">
+                    <label for="d">Coefficient d:</label>
+                    <input type="number" id="d" placeholder="e.g., 0">
+                </div>
+                <div class="input-group" id="e-group" style="display: none;">
+                    <label for="e">Coefficient e:</label>
+                    <input type="number" id="e" placeholder="e.g., 0">
+                </div>
+            </div>
+            <div class="input-group">
+                <label for="xValue">Value of x:</label>
+                <input type="number" id="xValue" placeholder="e.g., 2">
+            </div>
+            <div class="buttons" data-aos="fade-right">
+                <button class="btn" onclick="findRoots()">Find Roots</button>
+            </div>
+            <div class="output-group">
+                <label for="roots">Roots:</label>
+                <input type="text" id="roots" disabled>
+            </div>
+        </div>
+    </div>
+    <!-- AOS JS -->
+    <script src="https://cdnjs.cloudflare.com/ajax/libs/aos/2.3.4/aos.js"></script>
+    <script>
+        // Initialize AOS
+        AOS.init();
+    </script>
+    <script src="script.js"></script>
+</body>
+</html>
diff --git a/Calculators/Polynomial-Roots-Calculator/script.js b/Calculators/Polynomial-Roots-Calculator/script.js
@@ -0,0 +1,125 @@
+// Function to show/hide coefficient inputs based on selected degree
+function showCoefficientInputs() {
+    const degree = parseInt(document.getElementById('degree').value);
+    document.getElementById('d-group').style.display = degree >= 3 ? 'block' : 'none';
+    document.getElementById('e-group').style.display = degree >= 4 ? 'block' : 'none';
+}
+
+// Function to evaluate polynomial at a given value of x
+function evaluatePolynomial() {
+    const degree = parseInt(document.getElementById('degree').value);
+    const a = parseFloat(document.getElementById('a').value) || 0;
+    const b = parseFloat(document.getElementById('b').value) || 0;
+    const c = parseFloat(document.getElementById('c').value) || 0;
+    const d = degree >= 3 ? (parseFloat(document.getElementById('d').value) || 0) : 0;
+    const e = degree >= 4 ? (parseFloat(document.getElementById('e').value) || 0) : 0;
+    const x = parseFloat(document.getElementById('xValue').value);
+
+    if (isNaN(x)) {
+        alert('Please enter a valid number for the value of x.');
+        return;
+    }
+
+    let result = a * Math.pow(x, degree) + b * Math.pow(x, degree - 1) + c * Math.pow(x, degree - 2);
+    if (degree >= 3) result += d * Math.pow(x, degree - 3);
+    if (degree >= 4) result += e * Math.pow(x, degree - 4);
+
+    document.getElementById('result').value = result.toFixed(4);
+}
+
+// Function to find roots of polynomial
+function findRoots() {
+    const degree = parseInt(document.getElementById('degree').value);
+    const a = parseFloat(document.getElementById('a').value) || 0;
+    const b = parseFloat(document.getElementById('b').value) || 0;
+    const c = parseFloat(document.getElementById('c').value) || 0;
+    const d = degree >= 3 ? (parseFloat(document.getElementById('d').value) || 0) : 0;
+    const e = degree >= 4 ? (parseFloat(document.getElementById('e').value) || 0) : 0;
+
+    let roots = [];
+
+    if (degree === 2) {
+        roots = solveQuadratic(a, b, c);
+    } else if (degree === 3) {
+        roots = solveCubic(a, b, c, d);
+    } else if (degree === 4) {
+        roots = solveQuartic(a, b, c, d, e);
+    }
+
+    document.getElementById('roots').value = roots.length > 0 ? roots.join(', ') : 'No real roots';
+}
+
+// Function to solve quadratic equation
+function solveQuadratic(a, b, c) {
+    const discriminant = b * b - 4 * a * c;
+    if (discriminant > 0) {
+        const root1 = (-b + Math.sqrt(discriminant)) / (2 * a);
+        const root2 = (-b - Math.sqrt(discriminant)) / (2 * a);
+        return [root1.toFixed(4), root2.toFixed(4)];
+    } else if (discriminant === 0) {
+        const root = -b / (2 * a);
+        return [root.toFixed(4)];
+    } else {
+        const realPart = (-b / (2 * a)).toFixed(4);
+        const imaginaryPart = (Math.sqrt(-discriminant) / (2 * a)).toFixed(4);
+        return [`${realPart} + ${imaginaryPart}i`, `${realPart} - ${imaginaryPart}i`];
+    }
+}
+
+// Function to solve cubic equation (Cardano's method for simplicity)
+function solveCubic(a, b, c, d) {
+    // Normalized coefficients
+    b /= a;
+    c /= a;
+    d /= a;
+
+    const p = (3 * c - b * b) / 3;
+    const q = (2 * b * b * b - 9 * b * c + 27 * d) / 27;
+    const discriminant = Math.pow(q / 2, 2) + Math.pow(p / 3, 3);
+
+    let roots = [];
+    if (discriminant > 0) {
+        const u = Math.cbrt(-q / 2 + Math.sqrt(discriminant));
+        const v = Math.cbrt(-q / 2 - Math.sqrt(discriminant));
+        roots.push((u + v - b / 3).toFixed(4));
+    } else if (discriminant === 0) {
+        const u = Math.cbrt(-q / 2);
+        roots.push((2 * u - b / 3).toFixed(4));
+        roots.push((-u - b / 3).toFixed(4));
+    } else {
+        const r = Math.sqrt(Math.pow(-p / 3, 3));
+        const phi = Math.acos(-q / (2 * r));
+        for (let k = 0; k < 3; k++) {
+            const root = 2 * Math.cbrt(r) * Math.cos((phi + 2 * k * Math.PI) / 3) - b / 3;
+            roots.push(root.toFixed(4));
+        }
+    }
+    return roots;
+}
+
+// Function to solve quartic equation (Ferrari's method for simplicity)
+function solveQuartic(a, b, c, d, e) {
+    // Normalized coefficients
+    b /= a;
+    c /= a;
+    d /= a;
+    e /= a;
+
+    // Substitutions and solving steps (simplified)
+    const p = c - (3 * b * b) / 8;
+    const q = b * b * b / 8 - b * c / 2 + d;
+    const r = -3 * b * b * b * b / 256 + b * b * c / 16 - b * d / 4 + e;
+
+    const cubicRoots = solveCubic(1, p / 2, (p * p - 4 * r) / 16, -q * q / 64);
+    const z = cubicRoots[0]; // One real root
+
+    const u = Math.sqrt(z * z - 4 * r);
+    const v = Math.sqrt(2 * z - p);
+
+    const root1 = (-b / 4 + (u + v) / 2).toFixed(4);
+    const root2 = (-b / 4 + (u - v) / 2).toFixed(4);
+    const root3 = (-b / 4 - (u + v) / 2).toFixed(4);
+    const root4 = (-b / 4 - (u - v) / 2).toFixed(4);
+
+    return [root1, root2, root3, root4];
+}
diff --git a/Calculators/Polynomial-Roots-Calculator/style.css b/Calculators/Polynomial-Roots-Calculator/style.css
@@ -0,0 +1,78 @@
+body {
+    font-family: Arial, sans-serif;
+    display: flex;
+    justify-content: center;
+    align-items: center;
+    height: 100vh;
+    margin: 0;
+    background-color: rgb(244, 152, 81);
+    background: url("assets/boy.svg");
+    background-size: cover;
+}
+
+.calculator {
+    background: white;
+    padding: 20px;
+    border-radius: 8px;
+    box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);
+    max-width: 400px;
+    width: 110%;
+    box-shadow: 7px 0px 15px #e5d64b, -7px 0px 15px #faf9f9;
+}
+
+h1 {
+    text-align: center;
+    margin-bottom: 20px;
+   color: rgb(244, 152, 81);
+   width: 200%;
+   margin-left: -200px;
+   font-size: 50px;
+}
+
+.input-group, .output-group {
+    margin-bottom: 15px;
+}
+
+label {
+    display: block;
+    margin-bottom: 5px;
+}
+
+input[type="text"], input[type="number"], select {
+    width: calc(100% - 22px);
+    padding: 10px;
+    border: 1px solid #ccc;
+    border-radius: 4px;
+}
+
+.buttons {
+    display: flex;
+    justify-content: center;
+    gap: 10px;
+}
+
+.btn {
+    padding: 10px 20px;
+    background-color: #f6f8fa;
+    color: rgb(244, 152, 81);
+    border: none;
+    border-radius: 7px;
+    cursor: pointer;
+    box-shadow: 7px 0px 15px #e5d64b, -7px 0px 15px #e5d64b;
+    height:50%;
+    width: 50%;
+    font-size: 20px;
+    font-weight: bolder;
+}
+
+.btn:hover {
+    background-color: #f7f1f3;
+}
+
+#result, #roots {
+    width: calc(100% - 22px);
+    padding: 10px;
+    border: 1px solid #ccc;
+    border-radius: 4px;
+    background-color: #e9ecef;
+}
diff --git a/index.html b/index.html
@@ -1968,6 +1968,20 @@ <h3>Calculates various parameters of planetary motion using Kepler's laws.</h3>
                 </div>
             </div>
         </div>
+        <div class="box">
+            <div class="content">
+                <h2>Polynomial Roots Calculator</h2>
+                <h3>Calculates the real and imaginary roots of a given polynomial up to degree 2-4.</h3>
+                <div class="card-footer">
+                    <a href="./Calculators/Polynomial-Roots-Calculator/" target="_blank">
+                        <button>Try Now</button>
+                    </a>
+                    <a href="https://github.com/Rakesh9100/CalcDiverse/tree/main/Calculators/Polynomial-Roots-Calculator" title="Source Code" target="_blank">
+                        <img src="./assets/images/github.png" alt="Source Code"></img>
+                    </a>
+                </div>
+            </div>
+        </div>
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