MathDB

A polynomial

f(x)

of degree

2000

is given. It's known that

f(x^2-1)

has exactly

3400

real roots while

f(1-x^2)

has exactly

2700

real roots. Prove that there exist two real roots of

f(x)

such that the difference between them is less that

0.002

.
(А. Солынин)
Thanks to the user Vlados021 for translating the problem.

Problem Statement