MathDB
Poland 5

Source: IMO LongList 1959-1966 Problem 35

September 2, 2004
algebrapolynomialirrational numberrootsIMO ShortlistIMO Longlist

Problem Statement

Let ax3+bx2+cx+dax^{3}+bx^{2}+cx+d be a polynomial with integer coefficients a,a, b,b, c,c, dd such that adad is an odd number and bcbc is an even number. Prove that (at least) one root of the polynomial is irrational.
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