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Omni-MATH / Consider all polynomials P(x) with real coefficients that have the following property: for any two real numbers x and y one has |y²−P(x)|≤2|x| if and only if |x²−P(y)|≤2|y|. Determ…

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problem

Consider all polynomials P(x)P(x) with real coefficients that have the following property: for any two real numbers xx and yy one has |y2−P(x)|≤2|x|if and only if|x2−P(y)|≤2|y|.|y^2-P(x)|\le 2|x|\quad\text{if and only if}\quad |x^2-P(y)|\le 2|y|. Determine all possible values of P(0)P(0). [i]
Plain-text mathematical notation (without MathML)
Consider all polynomials P(x) with real coefficients that have the following property: for any two real numbers x and y one has |y²−P(x)|≤2|x| if and only if |x²−P(y)|≤2|y|. Determine all possible values of P(0).

[i]
Original LaTeX notation
Consider all polynomials $P(x)$ with real coefficients that have the following property: for any two real numbers $x$ and $y$ one has \[|y^2-P(x)|\le 2|x|\quad\text{if and only if}\quad |x^2-P(y)|\le 2|y|.\] Determine all possible values of $P(0)$.

[i]

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task_id
a3478292-b01f-587b-a806-c63b3976e525
task_key
test--a3478292-b01f-587b-a806-c63b3976e525
task_revision_id
1
config / split
/ test

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