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Found problems: 2

1986 Traian Lălescu, 1.3
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.
extremal polynom real analysis supremum polynomial function algebra

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