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253 lines
9.2 KiB
HTML
253 lines
9.2 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-old.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:02 GMT -->
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<head>
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<!-- #BeginEditable "doctitle" -->
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<title>Quadratic Equation Solver</title>
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<script language="JavaScript" type="text/javascript">
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<!-- Begin
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function calculate() {
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a = parseFloat(document.calculator.a.value);
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b = parseFloat(document.calculator.b.value);
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c = parseFloat(document.calculator.c.value);
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if (a == 0) {
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note = "Not a quadratic equation. 'a' shouldn't be zero.";
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ans1 = "NA";
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ans2 = "NA";
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} else {
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disc = b * b - 4 * a * c;
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if (disc < 0) {
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real = -b / (2 * a);
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imag = Math.sqrt(-disc) / (2 * a);
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note = "It has Complex Roots !";
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ans1 = real + " + " + Math.abs(imag) + "i";
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ans2 = real + " - " + Math.abs(imag) + "i";
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} else if (disc == 0) {
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note = "Only one answer !";
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ans1 = -b / (2 * a);
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ans2 = "NA";
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} else {
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note = "";
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ans1 = (-b + Math.sqrt(disc)) / (2 * a);
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ans2 = (-b - Math.sqrt(disc)) / (2 * a);
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}
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}
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formula = "";
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formula += NeatAdd(formula, a, "x²");
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formula += NeatAdd(formula, b, "x");
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formula += NeatAdd(formula, c, "");
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document.calculator.equn.value = formula + " = 0";
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document.calculator.disc.value = disc;
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document.calculator.ans1.value = ans1;
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document.calculator.ans2.value = ans2;
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document.calculator.note.value = note;
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}
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function NeatAdd(formula, x, varname) {
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s = "";
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if (formula.length == 0) {
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plus = "";
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} else {
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plus = " + ";
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}
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minus = " - ";
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if (x == 1) {
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if (varname.length == 0) {
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s = s + plus + "1";
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} else {
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s = s + plus + varname;
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}
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} else if (x == -1) {
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if (varname.length == 0) {
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s = s + minus + "1";
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} else {
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s = s + minus + varname;
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}
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} else if (x == 0) {} else if (x > 0) {
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s = s + plus + x + varname;
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} else {
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s = s + minus + Math.abs(x) + varname;
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}
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return s;
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}
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// End -->
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</script>
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<!-- #EndEditable -->
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<meta name="HandheldFriendly" content="true">
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<meta http-equiv="pics-label" content='(PICS-1.1 "http://www.classify.org/safesurf/" L gen true for "http://www.mathsisfun.com" r (SS~~000 1))'>
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<link rel="stylesheet" type="text/css" href="style3.css" />
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<script src="main3.js" type="text/javascript"></script>
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</head>
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<body id="bodybg">
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<div class="bg">
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<div id="stt"></div>
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<div id="hdr"></div>
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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="gtran"><script type="text/javascript">document.write(getTrans());</script></div>
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<div id="gplus"><script type="text/javascript">document.write(getGPlus());</script></div>
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<div id="adTopOuter" class="centerfull noprint">
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<div id="adTop">
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<script type="text/javascript">document.write(getAdTop());</script>
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</div>
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</div>
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<div id="adHide">
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<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
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<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
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<a href="about-ads.html">About Ads</a></div>
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</div>
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<div id="menuWide" class="menu">
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<script type="text/javascript">document.write(getMenu(0));</script>
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</div>
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<div id="linkto">
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<div id="linktort"><script type="text/javascript">document.write(getLinks());</script></div>
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</div>
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<div id="search" role="search"><script type="text/javascript">document.write(getSearch());</script></div>
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<div id="menuSlim" class="menu">
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<script type="text/javascript">document.write(getMenu(1));</script>
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</div>
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<div id="menuTiny" class="menu">
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<script type="text/javascript">document.write(getMenu(2));</script>
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</div>
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<div id="extra"></div>
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</div>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Quadratic Equation Solver</h1>
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<table border="0" align="center" cellpadding="3" width="570">
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<tr>
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<td>
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<p><i>If you have an equation of the form "<b>ax<sup>2</sup> + bx + c = 0</b>", we can solve it for you. </i><i>Just enter the
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factors a, b and c below, and press "Get Results"</i></p>
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</td>
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</tr>
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</table>
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<form name="calculator" id="calculator">
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<div class="simple">
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<table align="center" cellspacing="5">
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<tr>
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<td align="center" bgcolor="#FFFFFF" colspan="4"><img src="algebra/images/quadratic-equation.svg" alt="Quadratic Equation" /></td>
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</tr>
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<tr>
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<td class="large"> <font color="2222bb">a</font></td>
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<td class="large"> <font color="bb0000">b</font></td>
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<td class="large"> <font color="aa00aa">c</font></td>
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<td class="large"> </td>
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</tr>
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<tr>
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<td class="large">
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<input type="text" name="a" size="6" value="1" /> <b>x<sup>2</sup></b> + </td>
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<td class="large">
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<input type="text" name="b" size="6" value="0" /> <b>x</b> + </td>
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<td class="large">
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<input type="text" name="c" size="6" value="0" /> </td>
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<td class="large"><b>= 0</b></td>
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</tr>
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<tr>
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<td colspan="4" align="center">
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<input type="button" value="Get Results" onClick="calculate();" name="button" /> </td>
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</tr>
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</table>
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</div>
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<br />
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<br />
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<div class="simple">
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<table align="center">
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<tr>
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<td>
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<div align="right">Your Equation:</div>
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</td>
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<td>
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<input type="text" name="equn" size="50" /> </td>
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</tr>
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<tr>
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<td>
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<div align="right">Solution 1:</div>
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</td>
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<td>
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<input type="text" name="ans1" size="50" /> </td>
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</tr>
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<tr>
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<td>
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<div align="right">Solution 2:</div>
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</td>
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<td>
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<input type="text" name="ans2" size="50" /> </td>
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</tr>
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<tr>
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<td>
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<div align="right">Discriminant<b></b>:</div>
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</td>
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<td>
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<input type="text" name="disc" size="50" /> </td>
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</tr>
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<tr>
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<td>
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<div align="right">Note<b></b>:</div>
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</td>
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<td>
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<input type="text" name="note" size="50" /> </td>
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</tr>
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</table>
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</div>
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</form>
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<h2><br />
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Is it Quadratic?</h2>
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<p>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, So, the biggest clue is that highest power must be a square (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 width="500" border="0" align="center">
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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 width="176"><b>x<sup>2</sup> = 3x -1</b></td>
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<td width="158"><b>x<sup>2</sup> - 3x + 1 = 0</b></td>
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<td width="152">a=1, b=-3, c=1</td>
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</tr>
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<tr>
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<td width="176"><b>2(x<sup>2</sup> - 2x) = 5</b></td>
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<td width="158"><b>2x<sup>2</sup> - 4x - 5 = 0</b></td>
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<td width="152">a=2, b=-4, c=-5</td>
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</tr>
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<tr>
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<td width="176"><b>x(x-1) = 3</b></td>
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<td width="158"><b>x<sup>2</sup> - x - 3 = 0</b></td>
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<td width="152">a=1, b=-1, c=-3</td>
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</tr>
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<tr>
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<td width="176"><b>5 + 1/x - 1/x<sup>2</sup> = 0</b></td>
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<td width="158"><b>5x<sup>2</sup> + x - 1 = 0</b></td>
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<td width="152">a=5, b=1, c=-1</td>
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</tr>
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</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 align="center"><img src="algebra/images/quadratic-formula.svg" alt="x = [ -b plus minus square root of (b^2-4ac) ] / 2a" /></div>
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<p>The "±" means you 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. If it is positive, you will get two normal solutions, if it is zero you get just ONE solution, and if it is negative you get <i>imaginary</i> solutions.</p>
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<div class="related"> <a href="algebra/quadratic-equation.html">Quadratic Equations</a> <a href="algebra/index.html">Algebra Index</a> </div>
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<div id="copyrt">
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Copyright © 2017 MathsIsFun.com
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