A polynomial f(x) of degree 2000 is given. It's known that f(x2-1) has exactly 3400 real roots while f(1-x2) has exactly 2700 real roots. Prove that there exist two real roots of f(x) such that the difference between them is less than 0.002.
All of the following words are united by a common link, can you deduce what that link is?
Sesquipedalian, Esoteric, Noun, Exists, Visible, Word, Finite.