Question

If \(P(x)\) is a polynomial such that \[ P(x^2 + 1) = \{P(x)\}^2 + 1 \] then \(P'(0)\) is equal to

• A. 1
• B. 0
• C. -1
• D. None of these

Hint:

The intensity ratio of fine structure doublets follows statistical weights of initial states.

Answer 1

The Correct Option is A

Try \(P(x) = ax + b\), check if it satisfies the functional equation. You’ll find \(P(x) = x\) works. Then \(P'(x) = 1\), so \(P'(0) = 1\)