IMO Shortlist 1973 problem 16
Dodao/la:
arhiva2. travnja 2012. Given
![a, \theta \in \mathbb R, m \in \mathbb N](/media/m/d/1/6/d16485a5a72f74c7abf775bc436aadd5.png)
, and
![P(x) = x^{2m}- 2|a|^mx^m \cos \theta +a^{2m}](/media/m/e/3/3/e330ba44b41b02180aa83a5e31d0d8bd.png)
, factorize
![P(x)](/media/m/c/d/7/cd7664875343d44cd5f96a566b582b0e.png)
as a product of
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
real quadratic polynomials.
%V0
Given $a, \theta \in \mathbb R, m \in \mathbb N$, and $P(x) = x^{2m}- 2|a|^mx^m \cos \theta +a^{2m}$, factorize $P(x)$ as a product of $m$ real quadratic polynomials.
Izvor: Međunarodna matematička olimpijada, shortlist 1973