MathDB
Turkey NMO 2000 1st Round - P20 (Algebra)

Source:

July 25, 2012
algebrapolynomial

Problem Statement

For every real xx, the polynomial p(x)p(x) whose roots are all real satisfies p(x21)=p(x)p(x)p(x^2-1)=p(x)p(-x). What can the degree of p(x)p(x) be at most?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> There is no upper bound for the degree of p(x)<spanclass=latexbold>(E)</span> None <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ \text{There is no upper bound for the degree of } p(x) \qquad<span class='latex-bold'>(E)</span>\ \text{None}