System of polynomial equations
Source: South African Mathematics Olympiad 2021, Problem 5
August 11, 2021
algebrapolynomialsystem of equations
Problem Statement
Determine all polynomials , , , with real coefficients satisfying the simultaneous equations
\begin{align*}
b(x) c(x) + a(x) d(x) & = 0 \\
a(x) c(x) + (1 - x^2) b(x) d(x) & = x + 1.
\end{align*}