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IMO LongList 1967, Romania 2

Source: IMO LongList 1967, Romania 2

December 16, 2004
algebrapolynomialDiophantine equationparametric equationrootsIMO ShortlistIMO Longlist

Problem Statement

The equation x5+5λx4−x3+(λα−4)x2−(8λ+3)x+λα−2=0x^5 + 5 \lambda x^4 - x^3 + (\lambda \alpha - 4)x^2 - (8 \lambda + 3)x + \lambda \alpha - 2 = 0 is given. Determine α\alpha so that the given equation has exactly (i) one root or (ii) two roots, respectively, independent from λ.\lambda.
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