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 $P'(0) = 1$