This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

1986 Traian Lălescu, 1.2
Tags: polynomial function , algebra
Show that for any real numbers $ a,b, $ there exists $ c\in [-2,1] $ such that $ \big| c^3+ac+b\big| \ge 1. $

1986 Traian Lălescu, 1.3
Tags: algebra , real analysis , polynom , supremum , polynomial function , extremal
Let be four real numbers. Find the polynom of least degree such that two of these numbers are some locally extreme values, and the other two are the respective points of local extrema.