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RMO 2018 K2

  • Kerala and Tamil Nadu

Find the set of all real values of aa for which the real polynomial equation P(x)=x2−2ax+b=0P(x)=x^2-2ax+b=0 has real roots, given that P(0)⋅P(1)⋅P(2)≠0P(0)\cdot P(1)\cdot P(2)\neq 0 and P(0),P(1),P(2)P(0),P(1),P(2) form a geometric progression.

Dataset text AI-MO AoPS. Quoted with source.

Official text: Indian Regional Mathematical Olympiad 2018 official paper, page 1.

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