1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".
(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library – Reference Manual: Quadratic Equations</title>
<meta name="description" content="GNU Scientific Library – Reference Manual: Quadratic Equations">
<meta name="keywords" content="GNU Scientific Library – Reference Manual: Quadratic Equations">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Polynomials.html#Polynomials" rel="up" title="Polynomials">
<link href="Cubic-Equations.html#Cubic-Equations" rel="next" title="Cubic Equations">
<link href="Divided-Difference-Representation-of-Polynomials.html#Divided-Difference-Representation-of-Polynomials" rel="previous" title="Divided Difference Representation of Polynomials">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>
</head>
<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Quadratic-Equations"></a>
<div class="header">
<p>
Next: <a href="Cubic-Equations.html#Cubic-Equations" accesskey="n" rel="next">Cubic Equations</a>, Previous: <a href="Divided-Difference-Representation-of-Polynomials.html#Divided-Difference-Representation-of-Polynomials" accesskey="p" rel="previous">Divided Difference Representation of Polynomials</a>, Up: <a href="Polynomials.html#Polynomials" accesskey="u" rel="up">Polynomials</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Quadratic-Equations-1"></a>
<h3 class="section">6.3 Quadratic Equations</h3>
<a name="index-quadratic-equation_002c-solving"></a>
<dl>
<dt><a name="index-gsl_005fpoly_005fsolve_005fquadratic"></a>Function: <em>int</em> <strong>gsl_poly_solve_quadratic</strong> <em>(double <var>a</var>, double <var>b</var>, double <var>c</var>, double * <var>x0</var>, double * <var>x1</var>)</em></dt>
<dd><p>This function finds the real roots of the quadratic equation,
</p>
<div class="example">
<pre class="example">a x^2 + b x + c = 0
</pre></div>
<p>The number of real roots (either zero, one or two) is returned, and
their locations are stored in <var>x0</var> and <var>x1</var>. If no real roots
are found then <var>x0</var> and <var>x1</var> are not modified. If one real root
is found (i.e. if <em>a=0</em>) then it is stored in <var>x0</var>. When two
real roots are found they are stored in <var>x0</var> and <var>x1</var> in
ascending order. The case of coincident roots is not considered
special. For example <em>(x-1)^2=0</em> will have two roots, which happen
to have exactly equal values.
</p>
<p>The number of roots found depends on the sign of the discriminant
<em>b^2 - 4 a c</em>. This will be subject to rounding and cancellation
errors when computed in double precision, and will also be subject to
errors if the coefficients of the polynomial are inexact. These errors
may cause a discrete change in the number of roots. However, for
polynomials with small integer coefficients the discriminant can always
be computed exactly.
</p>
</dd></dl>
<dl>
<dt><a name="index-gsl_005fpoly_005fcomplex_005fsolve_005fquadratic"></a>Function: <em>int</em> <strong>gsl_poly_complex_solve_quadratic</strong> <em>(double <var>a</var>, double <var>b</var>, double <var>c</var>, gsl_complex * <var>z0</var>, gsl_complex * <var>z1</var>)</em></dt>
<dd>
<p>This function finds the complex roots of the quadratic equation,
</p>
<div class="example">
<pre class="example">a z^2 + b z + c = 0
</pre></div>
<p>The number of complex roots is returned (either one or two) and the
locations of the roots are stored in <var>z0</var> and <var>z1</var>. The roots
are returned in ascending order, sorted first by their real components
and then by their imaginary components. If only one real root is found
(i.e. if <em>a=0</em>) then it is stored in <var>z0</var>.
</p>
</dd></dl>
<hr>
<div class="header">
<p>
Next: <a href="Cubic-Equations.html#Cubic-Equations" accesskey="n" rel="next">Cubic Equations</a>, Previous: <a href="Divided-Difference-Representation-of-Polynomials.html#Divided-Difference-Representation-of-Polynomials" accesskey="p" rel="previous">Divided Difference Representation of Polynomials</a>, Up: <a href="Polynomials.html#Polynomials" accesskey="u" rel="up">Polynomials</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
</body>
</html>
|
