IMO Shortlist 1966 problem 35
Dodao/la:
arhiva2. travnja 2012. Let
![ax^{3}+bx^{2}+cx+d](/media/m/e/2/7/e27bb74e9f6c6be03f4f9b38940f68d8.png)
be a polynomial with integer coefficients
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
such that
![ad](/media/m/a/4/6/a464ca1c6fb195a1519b86e569397d63.png)
is an odd number and
![bc](/media/m/2/9/c/29c7b03a59f694881a988036e098bde2.png)
is an even number. Prove that (at least) one root of the polynomial is irrational.
%V0
Let $ax^{3}+bx^{2}+cx+d$ be a polynomial with integer coefficients $a,$ $b,$ $c,$ $d$ such that $ad$ is an odd number and $bc$ is an even number. Prove that (at least) one root of the polynomial is irrational.
Izvor: Međunarodna matematička olimpijada, shortlist 1966