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P32 [Algebra] - Turkish NMO 1st Round - 2003

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May 31, 2014
function

Problem Statement

The function ff satisfies f(x)+3f(1−x)=x2f(x)+3f(1-x)=x^2 for every real xx. If S={x∣f(x)=0}S=\{x \mid f(x)=0 \}, which one is true?
<spanclass=′latex−bold′>(A)</span><span class='latex-bold'>(A)</span> SS is an infinite set.
<spanclass=′latex−bold′>(B)</span><span class='latex-bold'>(B)</span> {0,1}⊂S\{0,1\} \subset S
<spanclass=′latex−bold′>(C)</span><span class='latex-bold'>(C)</span> S=ϕS=\phi
<spanclass=′latex−bold′>(D)</span><span class='latex-bold'>(D)</span> S={(3+3)/2,(3−3)/2}S = \{(3+\sqrt 3)/2, (3-\sqrt 3)/2\}
<spanclass=′latex−bold′>(E)</span><span class='latex-bold'>(E)</span> None of above
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