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P15 [Algebra] - Turkish NMO 1st Round - 2005

Source:

November 2, 2013
functionVieta

Problem Statement

For how many positive real numbers aa has the equation a2x2+ax+1−7a2=0a^2x^2 + ax+1-7a^2 = 0 two distinct integer roots?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> Infinitely many<spanclass=′latex−bold′>(E)</span> None of above <span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ 3 \qquad<span class='latex-bold'>(D)</span>\ \text{Infinitely many} \qquad<span class='latex-bold'>(E)</span>\ \text{None of above}
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