MathDB

4

Part of 1982 IMO Shortlist

Problems(1)

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

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

9/10/2010
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.
algebraDiophantine equationpolynomialparametric equationgeometric progressionIMO ShortlistIMO Longlist