Real Polynom
General polynomials unit, maintaining some distance from integer polynomials (though still overlapping slightly). Includes Vieta/Newton, multivariable polynomials, Lagrange interpolation, size arguments, differentiation.
Philosophy
This unit is all about dealing with arbitrary polynomials over the real numbers. The unit builds off and shares some problems with Symmetric Poly. Topics covered include Lagrange interpolation, factor theorem, Vieta's, finite differences, applications of differentiation.
This unit is definitely on the harder side for a D unit, many of the problems are quite difficult. Some units you can do after this unit are Irreducible and Int Poly.
The unit contains 80 clubs across 21 problems.
Notable Problems
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2002 USAMO/3 Difficult, elegant problem. Result is quite natural.
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2019 USEMO/2 9-pointer, functional equation from integer polynomials to integer polynomials, concerns integer roots.
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2015 ISL A6 Very difficult walkthrough. Good example of many core techniques introduced throughout the unit.