Difference between revisions of "Reciprocal equation"
From Encyclopedia of Mathematics
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$$a_0x^n+a_1x^{n-1}+\ldots+a_{n-1}x+a_n=0$$ | $$a_0x^n+a_1x^{n-1}+\ldots+a_{n-1}x+a_n=0$$ | ||
| − | 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 | + | 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 $z=x\pm1/x$. |
Revision as of 21:02, 25 October 2014
An equation of the form
$$a_0x^n+a_1x^{n-1}+\ldots+a_{n-1}x+a_n=0$$
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=34035
Reciprocal equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reciprocal_equation&oldid=34035
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article