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Determine a such that the equationhas four real roots in G.P

Source: IMO LongList 1982, P14 - IMO ShortList 1982, P2

September 10, 2010
algebraDiophantine equationpolynomialparametric equationgeometric progressionIMO ShortlistIMO Longlist

Problem Statement

Determine all real values of the parameter aa for which the equation 16x4−ax3+(2a+17)x2−ax+16=016x^4 -ax^3 + (2a + 17)x^2 -ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.
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