MathDB

monic polynomials

Source: Austria 1988

July 8, 2009

algebrapolynomialalgebra unsolved

Problem Statement

Determine all monic polynomials

p(x)

of fifth degree having real coefficients and the following property: Whenever

a

is a (real or complex) root of

p(x)

, then so are

\frac{1}{a}

and 1\minus{}a.