Question 161
Find all polynomials $P(x)$, $Q(x)$ with real coefficients, such that for each real number $a$, $P(a)$ is the solution of the following equation
$$
x^{2023} + Q(a)x^2 + (a^{2024} + a)x + a^3 + 2025a = 0.
$$
$$
x^{2023} + Q(a)x^2 + (a^{2024} + a)x + a^3 + 2025a = 0.
$$