Properties
Reciprocal polynomials have several connections with their original polynomials, including:
- α is a root of polynomial p if and only if α-1 is a root of p*.
- If p(x) ≠ x then p is irreducible if and only if p* is irreducible.
- p is primitive if and only if p* is primitive.
Other properties of reciprocal polynomials may be obtained, for instance:
- If a polynomial is self-reciprocal and irreducible then it must have even degree.
Read more about this topic: Reciprocal Polynomial
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—Ralph Waldo Emerson (1803–1882)
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