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The first problem of the first Spanish Math Olympiad (1963-)

Source: http://www.olimpiadamatematica.es/platea.pntic.mec.es/_csanchez/olimp_1963-2004/OME2004.pdf

November 14, 2016
Polynomialsalgebra

Problem Statement

Given the equation x2+ax+1=0x^2+ax+1=0, determine:
a) The interval of possible values for aa where the solutions to the previous equation are not real. b) The loci of the roots of the polynomial, when aa is in the previous interval.
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