A Surprisingly Challenging Quadratic Polynomial Problem

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I go over a surprisingly challenging math competition problem involving quadratic polynomials.

IMO 2023:

IMO 2022:

IMO 2021:

IMO 2020:

IMO 2019:

IMO 2018:

IMO 1977:

IMO 1961:
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I used Lagrange interpolation and I got a last inequality quite easily. It may be an another solution.

TaoTao
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Thanks 🎉 I love the way you explain. Love and Respect from India

nirupam