Question 60
Consider all polynomials $P(x)$ with real coefficients that have the following property: for all real $x$ and $y$ one has
$$
|y^2 - P(x)| \le 2x \iff |x^2 - P(y)| \le 2|y|.
$$
Determine all possible values of $P(0)$.
Editorial metadata note: Metadata discrepancy: the dataset year is 2014, while booklet_year is 2015. The title follows dataset classification, not a verified Belarus 2014 event date.
$$
|y^2 - P(x)| \le 2x \iff |x^2 - P(y)| \le 2|y|.
$$
Determine all possible values of $P(0)$.
Editorial metadata note: Metadata discrepancy: the dataset year is 2014, while booklet_year is 2015. The title follows dataset classification, not a verified Belarus 2014 event date.