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| author | altaf-creator <athaalaa@gmail.com> | 2023-09-25 20:18:57 +0700 |
|---|---|---|
| committer | altaf-creator <athaalaa@gmail.com> | 2023-09-25 20:18:57 +0700 |
| commit | 18670260285d25b14921a89fae60089da334c921 (patch) | |
| tree | dbd0d0a17a7704e963504744e21a273b9c374b3b /lessons-locked/matematika/quadratic-equation | |
| parent | 7420ea9926c6cca698efa670d837a1cd753c4931 (diff) | |
Unlocked website, added rationalising roots
Diffstat (limited to 'lessons-locked/matematika/quadratic-equation')
| -rw-r--r-- | lessons-locked/matematika/quadratic-equation/finding-suitable.html | 117 | ||||
| -rw-r--r-- | lessons-locked/matematika/quadratic-equation/index.html | 277 |
2 files changed, 0 insertions, 394 deletions
diff --git a/lessons-locked/matematika/quadratic-equation/finding-suitable.html b/lessons-locked/matematika/quadratic-equation/finding-suitable.html deleted file mode 100644 index 9e13f01..0000000 --- a/lessons-locked/matematika/quadratic-equation/finding-suitable.html +++ /dev/null @@ -1,117 +0,0 @@ -<!DOCTYPE html> -<html lang="en"> - -<head> - <meta charset="UTF-8"> - <meta http-equiv="X-UA-Compatible" content="IE=edge"> - <meta name="viewport" content="width=device-width, initial-scale=1.0"> - <link rel="stylesheet" href="/style.css"> - <link rel="icon" href="/assets/images/master.svg"> - <title>Al Azhar 9th Grade Lesson Notes</title> - <link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> - <link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> - <link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> - <link rel="manifest" href="/site.webmanifest"> - <script src="https://kit.fontawesome.com/d279a1f519.js" crossorigin="anonymous"></script> - <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.css" - integrity="sha384-pRsDYiLLocCzWnUN/YEr9TBTTaZOUi5x8adKfqi6Qt44lDaFkoP++x1j2ohSMtdf" crossorigin="anonymous"> - <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.js" - integrity="sha384-tMzugJpfLv7v0f+KXzNMqNCC6sVzLMM3sCnZDgzy0lcO/0h3sAkEBg/URFcV0JpE" - crossorigin="anonymous"></script> -</head> - -<body> - <div class="fixed-top-btn-container" id="topbtn"> - <a class="fixed-top-btn menu-btn" onclick="toggleNav()" href="javascript:void(0)"><i - class="fa-solid fa-bars"></i></a> - <a href="../" class="fixed-top-btn back-btn"><i class="fa-solid fa-chevron-left"></i></a> - </div> - <div id="console"></div> - <div id="sidebar"> - <div> - <a href="/index.html"> - <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> - </a> - - <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> - </div> - - <div> - <a href="/about/author.html" class="sidebar-link link">About the Author</a> - <a href="/about/school.html" class="sidebar-link link">About School</a> - <a href="/lessons" class="sidebar-link link">Lessons</a> - - - <hr class="divider"> - <div id="toc"> - <h4>Table of Contents</h4> - </div> - </div> - </div> - - <div class="banner-container" id="banner"> - <div class="banner-bg" id="img-supplies"></div> - <div class="gradient-bg"></div> - <div class="banner-text-container"> - <h1 class="banner-text" id="banner-txt">Quadratic Equation: Finding the suitable factor</h1> - <h3 class="banner-text" id="banner-txt">Chapter 2 sub-page</h3> - </div> - </div> - - <div class="chip-container" id="chip-container"> - <div class="chip" title="Beware of mistakes. Please report to me (Altaf) if you caught a mistake here."><span>❓ Unchecked by Professionals</span></div> - </div> - - <div id="main"> - <section> - <p><strong><a href="/lessons/matematika/quadratic-equation/" class="link">← Go back to Main Lesson</a></strong></p> - Firstly, lets use this equation. <br> - <span id="m1"></span><br> - <h1 id="steps">Step-by-step</h1> - <ol> - <li>Find the factors of <span class="math-font">c</span>, which in this equation, <span class="math-font">c = </span><span class="math-font-main">30</span>.</li> - <li>The factors of 30 are: - <ul> - <li>1, 30</li> - <li>2, 15</li> - <li>3, 10</li> - <li>5, 6</li> - </ul> - </li> - <li>Lets define that the first and second factors are <span class="math-font">y<sub>1, 2</sub></span>. To find the suitable factors for the equation, you need to check if; - <ul> - <li><span id="m2"></span>, and</li> - <li><span id="m3"></span></li> - </ul> - </li> - <li>Check for each of the factors. We end up with 5 and 6. <br> <span id="m4"></span></li> - <li>So, the answer is <strong><span class="math-font-main">5 & 6</span></strong></li> - </ol> - <p><strong><a href="/lessons/matematika/quadratic-equation/" class="link">← Go back to Main Lesson</a></strong></p> - <script defer> - var element1 = document.getElementById("m1"); - var element2 = document.getElementById("m2"); - var element3 = document.getElementById("m3"); - var element4 = document.getElementById("m4"); - - katex.render(String.raw`x^2 + 11x + 30 = 0`, element1, { - throwOnError: false - }); - katex.render(String.raw`y_1 + y_2 = b`, element2, { - throwOnError: false - }); - katex.render(String.raw`y_1 \times y_2 = c`, element3, { - throwOnError: false - }); - katex.render(String.raw`5 \times 6 = 30\\5 + 6 = 11`, element4, { - throwOnError: false - }); - </script> - </section> - </div> - - <script src="/scripts/toc.js"></script> - <script src="/scripts/sidebar.js"></script> -</body> - -</html>
\ No newline at end of file diff --git a/lessons-locked/matematika/quadratic-equation/index.html b/lessons-locked/matematika/quadratic-equation/index.html deleted file mode 100644 index 288d0d9..0000000 --- a/lessons-locked/matematika/quadratic-equation/index.html +++ /dev/null @@ -1,277 +0,0 @@ -<!DOCTYPE html> -<html lang="en"> - -<head> - <meta charset="UTF-8"> - <meta http-equiv="X-UA-Compatible" content="IE=edge"> - <meta name="viewport" content="width=device-width, initial-scale=1.0"> - <link rel="stylesheet" href="/style.css"> - <link rel="icon" href="/assets/images/master.svg"> - <title>Al Azhar 9th Grade Lesson Notes</title> - <link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> - <link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> - <link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> - <link rel="manifest" href="/site.webmanifest"> - <script src="https://kit.fontawesome.com/d279a1f519.js" crossorigin="anonymous"></script> - <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.css" - integrity="sha384-pRsDYiLLocCzWnUN/YEr9TBTTaZOUi5x8adKfqi6Qt44lDaFkoP++x1j2ohSMtdf" crossorigin="anonymous"> - <script src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.js" - integrity="sha384-tMzugJpfLv7v0f+KXzNMqNCC6sVzLMM3sCnZDgzy0lcO/0h3sAkEBg/URFcV0JpE" - crossorigin="anonymous"></script> -</head> - -<body> - <div class="fixed-top-btn-container" id="topbtn"> - <a class="fixed-top-btn menu-btn" onclick="toggleNav()" href="javascript:void(0)"><i - class="fa-solid fa-bars"></i></a> - <a href="../" class="fixed-top-btn back-btn"><i class="fa-solid fa-chevron-left"></i></a> - </div> - <div id="console"></div> - <div id="sidebar"> - <div> - <a href="/index.html"> - <img src="/assets/images/master.svg" alt="" class="sidebar-logo"> - </a> - - <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3> - </div> - - <div> - <a href="/about/author.html" class="sidebar-link link">About the Author</a> - <a href="/about/school.html" class="sidebar-link link">About School</a> - <a href="/lessons" class="sidebar-link link">Lessons</a> - - - <hr class="divider"> - <div id="toc"> - <h4>Table of Contents</h4> - </div> - </div> - </div> - - <div class="banner-container" id="banner"> - <div class="banner-bg" id="img-supplies"></div> - <div class="gradient-bg"></div> - <div class="banner-text-container"> - <h1 class="banner-text" id="banner-txt">Quadratic Equation: The Introduction</h1> - <h3 class="banner-text" id="banner-txt">Chapter 2</h3> - </div> - </div> - - <div class="chip-container" id="chip-container"> - <div class="chip" title="Beware of mistakes. Please report to me (Altaf) if you caught a mistake here."><span>❓ Unchecked by Professionals</span></div> - </div> - - <div id="main"> - <section> - <h1 id="introduction">Introduction</h1> - In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x - represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.<sup>[<a - href="#reference-1" class="link-compact">1</a>]</sup> - <h2 id="introduction--formula">Formula / Format</h2> - <span class="math-font">ax<sup>2</sup> + bx + c = 0</span> - <p> - <span class="math-font">a, b, c</span> = known numbers, where a ≠ 0 <br> - <span class="math-font">x</span> = the unknown, or the root - </p> - <h2 id="introduction--exercise">Exercises</h2> - <h3>Finding the roots with factorisation.</h3> - <ol> - <li> - <span id="q1.1.1"></span> - <p> - <hr> - <span>To find the answer, we need to find the factors of c that is suitable for b and c. <a href="finding-suitable.html" class="link">What and how do I find the suitable factors?</a></span><br> - <span>The suitable factor for the equation are <b>2 and -3</b>. </span><br> - <span>Then, insert each numbers to this formula: <span id="q1.1.2"></span>, where <span - class="math-font">y</span> is the factor.</span><br><br> - <span id="q1.1.3"></span><br><span id="q1.1.31"></span><br> - <hr> - <strong>So, the answer is <span id="q1.1.4"></span></strong> - </p> - <script defer> - var element1 = document.getElementById("q1.1.1"); - var element2 = document.getElementById("q1.1.2"); - var element3 = document.getElementById("q1.1.3"); - var element31 = document.getElementById("q1.1.31"); - var element4 = document.getElementById("q1.1.4"); - - katex.render(String.raw`x^2 - 1x - 6 = 0`, element1, { - throwOnError: false - }); - katex.render(String.raw`x + y`, element2, { - throwOnError: false - }); - katex.render(String.raw` - \begin{aligned} - x + 2 &= 0\\ - x &= -2\\ - \end{aligned} - `, element3, { - throwOnError: true - }); katex.render(String.raw` - \begin{aligned} - x - 3 &= 0\\ - x &= 3 - \end{aligned} - `, element31, { - throwOnError: true - }); - katex.render(String.raw`x = \{-2, 3\}`, element4, { - throwOnError: false - }); - </script> - </li> - <li> - <p> - <span id="q1.2.1"></span><br> - <span><strong>Factors:</strong> <span class="math-font">2, 4</span></span><br> - <hr> - <span id="q1.2.2"></span><br> - <span id="q1.2.3"></span><br> - <hr> - <span id="q1.2.4"></span><br> - </p> - <script defer> - var element1 = document.getElementById("q1.2.1"); - var element2 = document.getElementById("q1.2.2"); - var element3 = document.getElementById("q1.2.3"); - var element4 = document.getElementById("q1.2.4"); - - katex.render(String.raw`x^2 + 6x + 8 = 0`, element1, { - throwOnError: false - }); - katex.render(String.raw` - \begin{aligned} - x + 2 &= 0\\ - x &= -2\\ - \end{aligned} - `, element2, { - throwOnError: true - }); katex.render(String.raw` - \begin{aligned} - x + 4 &= 0\\ - x &= 4 - \end{aligned} - `, element3, { - throwOnError: true - }); - katex.render(String.raw`x = \{-2, -4\}`, element4, { - throwOnError: false - }); - </script> - </li> - </ol> - <h1 id="relation-algebra">Relation between Quadratic Equation and Algebraic Expressions</h1> - <p>This is an algebraic expression → <span id="m0"></span>. You can turn that into a quadratic equation.</p> - <span id="m1"></span> - <script> - const m0 = document.getElementById("m0"); - const m1 = document.getElementById("m1"); - - katex.render(String.raw`(x + 5)(x + 7)`, m0, { - throwOnError: false - }); - katex.render(String.raw` - \begin{aligned} - (x + 5)(x + 7) &= x^2 + 5x + 7x + 35&\\ - &= x^2 + 12x + 35&\larr\textnormal{quadratic equation 😱😱} - \end{aligned} - `, m1, { - throwOnError: true - }); - </script> - <h1 id="all-about-roots">Quadratic Equation's Root Operations</h1> - <h2 id="finding-qe">Finding Quadratic Equation with Roots</h2> - <p>You can use the formula below to find a Quadratic Equation with 2 roots.</p> - <span id="m2"></span><span>, where <span class=math-font>x<sub>1, 2</sub></span> are the roots.</span><br> - <p> - <strong>Example:</strong><br><br> - <span id="m3"></span> - </p> - <script> - const m2 = document.getElementById("m2"); - const m3 = document.getElementById("m3"); - - katex.render(String.raw`(x - x_1)(x - x_2) = 0`, m2, { - throwOnError: false - }); - katex.render(String.raw` - \begin{aligned} - (x - x_1)(x - x_2) &= 0\\ - (x - (-3))(x - 4) &= 0\\ - (x + 3))(x - 4) &= 0\\ - x^2 - 4x + 3x - 12 &= 0\\ - x^2 - x - 12 &= 0 - \end{aligned} - `, m3, { - throwOnError: true - }); - </script> - <h2 id="operations">Quadratic Root's Mathematical Operations</h2> - <h3 id="operations--formulas">Formulas</h3> - <p id="m4"></p> - <p id="m5"></p> - <h3 id="operations--examples">Examples</h3> - <ol> - <li> - <p>Diketahui persamaan kuadrat <span id="q1"></span>, memiliki akar-akar persamaan kuadrat <span class="math-font">x<sub>1</sub></span> dan <span class="math-font">x<sub>2</sub></span>. Jika <span class="math-font">x<sub>1</sub> < x<sub>2</sub></span>, maka tentukan: - <ol type="a"> - <li><span class="math-font">x<sub>1</sub> + x<sub>2</sub></span></li> - <li><span class="math-font">x<sub>1</sub> × x<sub>2</sub></span></li> - </ol> - </p> - <hr> - <ol type="a"> - <li><span id="a1"></span></li> - <li><span id="a2"></span></li> - </ol> - </li> - </ol> - <script> - const m4 = document.getElementById("m4"); - const m5 = document.getElementById("m5"); - const q1 = document.getElementById("q1"); - const a1 = document.getElementById("a1"); - const a2 = document.getElementById("a2"); - - katex.render(String.raw`x_1 + x_2 = \dfrac{-b}{a}`, m4, { - throwOnError: false - }); - katex.render(String.raw`x_1 \times x_2 = \dfrac{c}{a}`, m5, { - throwOnError: false - }); - katex.render(String.raw`2x^2 + 7x + 3 = 0`, q1, { - throwOnError: false - }); - katex.render(String.raw` - \begin{aligned} - x_1 + x_2 &= \dfrac{-b}{a}\\ - &= \dfrac{-7}{2}\\ - \end{aligned} - `, a1, { - throwOnError: true - }); - katex.render(String.raw` - \begin{aligned} - x_1 \times x_2 &= \dfrac{c}{a}\\ - &= \dfrac{3}{2}\\ - \end{aligned} - `, a2, { - throwOnError: true - }); - </script> - <h1>References</h1> - <ol> - <li id="reference-1" tabindex="-1">Quadratic Equation - The English Wikipedia, <a - href="https://en.wikipedia.org/wiki/Quadratic_equation" - class="link">https://en.wikipedia.org/wiki/Quadratic_equation</a></li> - </li> - </section> - </div> - - <script src="/scripts/toc.js"></script> - <script src="/scripts/sidebar.js"></script> -</body> - -</html>
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