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148 lines
5.9 KiB
HTML
148 lines
5.9 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/quadratic-equation-solver.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:30:18 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<title>Quadratic Equation Solver</title>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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</head>
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="search" role="search"></div>
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<article id="content" role="main">
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<h1 class="center">Quadratic Equation Solver</h1>
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<p class="center"><i>We can help you solve an equation of the form "<b>ax<sup>2</sup> + bx + c = 0</b>"</i> <i><br>
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Just enter the
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values of a, b and c below</i>:</p><br>
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<div class="script" style="height: 500px;">
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algebra/images/quadratic-solver.js
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</div>
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<h2>Is it Quadratic?</h2>
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<p class="center"><img src="algebra/images/quadratic-equation.svg" alt="Quadratic Equation" height="33" width="301"></p>
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<p class="center">Only if it can be put in the form <i><b>ax<sup>2</sup> + bx + c = 0</b></i>, and <i><b>a</b></i> is <i>not zero</i>.</p>
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<p>The name comes from "quad" meaning square, as the variable is <a href="square-root.html">squared</a> (in other words <i><b>x<sup>2</sup></b></i>).</p>
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<p>These are all quadratic equations in disguise:</p>
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<div class="beach">
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<table align="center" width="500" border="0">
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<tbody>
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<tr>
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<th width="176">In disguise</th>
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<th width="158">In standard form</th>
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<th width="152">a, b and c</th>
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</tr>
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<tr>
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<td style="width:176px;"><b>x<sup>2</sup> = 3x -1</b></td>
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<td style="width:158px;"><b>x<sup>2</sup> - 3x + 1 = 0</b></td>
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<td style="width:152px;">a=1, b=-3, c=1</td>
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</tr>
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<tr>
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<td style="width:176px;"><b>2(x<sup>2</sup> - 2x) = 5</b></td>
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<td style="width:158px;"><b>2x<sup>2</sup> - 4x - 5 = 0</b></td>
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<td style="width:152px;">a=2, b=-4, c=-5</td>
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</tr>
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<tr>
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<td style="width:176px;"><b>x(x-1) = 3</b></td>
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<td style="width:158px;"><b>x<sup>2</sup> - x - 3 = 0</b></td>
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<td style="width:152px;">a=1, b=-1, c=-3</td>
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</tr>
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<tr>
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<td style="width:176px;"><b>5 + 1/x - 1/x<sup>2</sup> = 0</b></td>
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<td style="width:158px;"><b>5x<sup>2</sup> + x - 1 = 0</b></td>
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<td style="width:152px;">a=5, b=1, c=-1</td>
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</tr>
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</tbody></table>
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</div>
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<h2>How Does this Work?</h2>
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<p>The solution(s) to a quadratic equation can be calculated using the <b>Quadratic Formula</b>:</p>
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<div class="center"><img src="algebra/images/quadratic-formula.svg" alt="x = [ -b plus minus square root of (b^2-4ac) ] / 2a" height="79" width="286"></div>
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<p>The "±" means we need to do a plus AND a minus, so there are normally TWO solutions !</p>
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<p>The blue part (<b>b<sup>2</sup> - 4ac</b>) is called the "discriminant", because it can "discriminate" between the possible types of answer:</p>
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<ul>
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<li>when it is positive, we get two real solutions,</li>
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<li>when it is zero we get just ONE solution,</li>
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<li>when it is negative we get <i><a href="numbers/complex-numbers.html">complex</a></i> solutions.</li>
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</ul>
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<p>Learn more at <a href="algebra/quadratic-equation.html">Quadratic Equations</a></p>
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<p> </p>
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<p>Note: you can still access the old version <a href="quadratic-equation-solver-old.html">here</a>.</p>
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<div class="related">
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<a href="algebra/quadratic-equation.html">Quadratic Equations</a>
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<a href="algebra/factoring-quadratics.html">Factoring Quadratics</a>
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<a href="algebra/completing-square.html">Completing the Square</a>
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<a href="algebra/quadratic-equation-graphing.html">Graphing Quadratic Equations</a>
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<a href="algebra/quadratic-equation-real-world.html">Real World Examples of Quadratic Equations</a>
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<a href="algebra/quadratic-equation-derivation.html">Derivation of Quadratic Equation</a>
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<a href="algebra/index.html">Algebra Index</a>
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</div>
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<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
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