\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find all \(a, b \in \mathbb{R}\) such that \(X^2 + 1\) divides \(X^4 + a X^3 + b X^2 + a X + 1\) in \(\mathbb{R}[X]\). Hint. Write the quotient as \(X^2 + p X + q\) with \(p, q \in \mathbb{R}\) and identify coefficients.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.