Let \( f(x) \) be a polynomial function satisfying \( f(x)+f\left(\frac{1}{x}\right)=f(x) f\left....

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Let \( f(x) \) be a polynomial function satisfying
\( \mathrm{P} \)
\( f(x)+f\left(\frac{1}{x}\right)=f(x) f\left(\frac{1}{x}\right) \) for all \( x \neq 0 \).
If \( f(5)=126 \) and \( a, b, c \) are in G.P., then \( f^{\prime}(a), f^{\prime}(b) \), \( f^{\prime}(c) \) are in
(1) A.P.
(2) G.P.
(3) H.P.
(4) none of these


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