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Index Page rquad_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       rquad_c ( Roots of a quadratic equation )

       void rquad_c ( SpiceDouble  a,
                      SpiceDouble  b,
                      SpiceDouble  c,
                      SpiceDouble  root1[2],
                      SpiceDouble  root2[2] )

#### Abstract

       Find the roots of a quadratic equation.

#### Required_Reading

       None.

#### Keywords

       MATH
       POLYNOMIAL
       ROOT

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       a          I   Coefficient of quadratic term.
       b          I   Coefficient of linear term.
       c          I   Constant.
       root1      O   Root built from positive discriminant term.
       root2      O   Root built from negative discriminant term.

#### Detailed_Input

       a,
       b,
       c           are the coefficients of a quadratic polynomial

                        2
                      ax   +   bx   +   c.

#### Detailed_Output

       root1,
       root2       are the roots of the equation,

                         2
                       ax   +   bx   +   c   =  0.

                   root1 and root2 are both arrays of length 2. The
                   first element of each array is the real part of a
                   root; the second element contains the complex part
                   of the same root.

                   When a is non-zero, root1 represents the root

                                    _____________
                                   /  2
                      - b   +    \/  b    -   4ac
                      ---------------------------
                                    2a

                   and root2 represents the root

                                    _____________
                                   /  2
                      - b   -    \/  b    -   4ac
                      --------------------------- .
                                    2a

                   When a is zero and b is non-zero, root1 and root2
                   both represent the root

                      - c / b.

#### Parameters

       None.

#### Exceptions

       1)  If the input coefficients `a' and `b' are both zero, the error
           SPICE(DEGENERATECASE) is signaled. The output arguments are not
           modified.

#### Files

       None.

#### Particulars

       None.

#### Examples

       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) Humor us and suppose we want to compute the "golden ratio."

          The quantity `r' is defined by the equation

             1/r = r/(1-r),

          which is equivalent to

              2
             r   +  r  -  1  =  0.

          The following code example does the job.

          Example code begins here.

          /.
             Program rquad_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {
             /.
             Local variables.
             ./
             SpiceDouble             root1 [ 2 ];
             SpiceDouble             root2 [ 2 ];

             /.
             Compute "golden ratio."  The root we want,

                        ___
                       /
                -1 + \/  5
                -----------,
                     2

             is contained in root1.
             ./
             rquad_c ( 1., 1., -1., root1, root2 );

             /.
             Print the results.
             ./
             printf ( "The \"golden ratio\" is %f\n", root1[0] );

             return ( 0 );

          }

          When this program was executed on a Mac/Intel/cc/64-bit
          platform, the output was:

          The "golden ratio" is 0.618034

       2) Calculate the roots of the following quadratic equation:

              2
             x  + 2x + 3 = 0

          Example code begins here.

          /.
             Program rquad_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {
             /.
             Local variables.
             ./
             SpiceDouble             root1 [ 2 ];
             SpiceDouble             root2 [ 2 ];

             /.
             Let's do one with imaginary roots just for fun.
             ./

             rquad_c ( 1.,  2.,  3.,  root1,  root2 );

             printf ( "Root #1: %12.7f %12.7f\n", root1[0], root1[1] );
             printf ( "Root #2: %12.7f %12.7f\n", root2[0], root2[1] );

             return ( 0 );
          }

          When this program was executed on a Mac/Intel/cc/64-bit
          platform, the output was:

          Root #1:   -1.0000000    1.4142136
          Root #2:   -1.0000000   -1.4142136

#### Restrictions

       1)  No checks for overflow of the roots are performed.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)

#### Version

       -CSPICE Version 1.0.1, 04-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.

           Created complete code examples from existing code fragments.

       -CSPICE Version 1.0.0, 13-JUN-1999 (NJB)

#### Index_Entries

       roots of a quadratic equation

#### Link to routine rquad_c source file rquad_c.c

    Fri Dec 31 18:41:11 2021