March Break 2024 - Problem 10

A polynomial P(x) of degree 2024 with real coefficients satisfies the following conditions:

• P(x)=(x-1)^{240}\cdot Q(x) for a polynomial Q(x) with real coefficients, such that Q(1) \neq 0.

• In P(x), the coefficient of the x^i term is equal to the coefficient of the x^{2024-i} term for nonnegative integers i <1012.

Given that all the roots of P(x) are real, how many of them are greater than 1?