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<title>GNU Scientific Library &ndash; Reference Manual: Cubic Equations</title>

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<a name="Cubic-Equations"></a>
<div class="header">
<p>
Next: <a href="General-Polynomial-Equations.html#General-Polynomial-Equations" accesskey="n" rel="next">General Polynomial Equations</a>, Previous: <a href="Quadratic-Equations.html#Quadratic-Equations" accesskey="p" rel="previous">Quadratic Equations</a>, Up: <a href="Polynomials.html#Polynomials" accesskey="u" rel="up">Polynomials</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Cubic-Equations-1"></a>
<h3 class="section">6.4 Cubic Equations</h3>
<a name="index-cubic-equation_002c-solving"></a>

<dl>
<dt><a name="index-gsl_005fpoly_005fsolve_005fcubic"></a>Function: <em>int</em> <strong>gsl_poly_solve_cubic</strong> <em>(double <var>a</var>, double <var>b</var>, double <var>c</var>, double * <var>x0</var>, double * <var>x1</var>, double * <var>x2</var>)</em></dt>
<dd>
<p>This function finds the real roots of the cubic equation,
</p>
<div class="example">
<pre class="example">x^3 + a x^2 + b x + c = 0
</pre></div>

<p>with a leading coefficient of unity.  The number of real roots (either
one or three) is returned, and their locations are stored in <var>x0</var>,
<var>x1</var> and <var>x2</var>.  If one real root is found then only <var>x0</var>
is modified.  When three real roots are found they are stored in
<var>x0</var>, <var>x1</var> and <var>x2</var> in ascending order.  The case of
coincident roots is not considered special.  For example, the equation
<em>(x-1)^3=0</em> will have three roots with exactly equal values.  As
in the quadratic case, finite precision may cause equal or
closely-spaced real roots to move off the real axis into the complex
plane, leading to a discrete change in the number of real roots.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fpoly_005fcomplex_005fsolve_005fcubic"></a>Function: <em>int</em> <strong>gsl_poly_complex_solve_cubic</strong> <em>(double <var>a</var>, double <var>b</var>, double <var>c</var>, gsl_complex * <var>z0</var>, gsl_complex * <var>z1</var>, gsl_complex * <var>z2</var>)</em></dt>
<dd>
<p>This function finds the complex roots of the cubic equation,
</p>
<div class="example">
<pre class="example">z^3 + a z^2 + b z + c = 0
</pre></div>

<p>The number of complex roots is returned (always three) and the locations
of the roots are stored in <var>z0</var>, <var>z1</var> and <var>z2</var>.  The roots
are returned in ascending order, sorted first by their real components
and then by their imaginary components.
</p>
</dd></dl>





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