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Difference between revisions of "Reciprocal equation"

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An equation of the form
 
An equation of the form
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080080/r0800801.png" /></td> </tr></table>
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$$a_0x^n+a_1x^{n-1}+\dotsb+a_{n-1}x+a_n=0$$
  
in which the coefficients located at equal distances from the beginning and from the end are equal: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080080/r0800802.png" />. A reciprocal equation of degree <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080080/r0800803.png" /> may be be reduced to an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080080/r0800804.png" />-th degree equation by putting <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080080/r0800805.png" />.
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in which the coefficients located at equal distances from the beginning and from the end are equal: $a_i=a_{n-i}$. A reciprocal equation of degree $2n$ may be reduced to an $n$-th degree equation by putting $z=x\pm1/x$.
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[[Category:Field theory and polynomials]]

Latest revision as of 12:43, 14 February 2020

An equation of the form

$$a_0x^n+a_1x^{n-1}+\dotsb+a_{n-1}x+a_n=0$$

in which the coefficients located at equal distances from the beginning and from the end are equal: $a_i=a_{n-i}$. A reciprocal equation of degree $2n$ may be reduced to an $n$-th degree equation by putting $z=x\pm1/x$.

How to Cite This Entry:
Reciprocal equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reciprocal_equation&oldid=14468
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article