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Let (f(x+y)-f(x))/2 = (f(y)-a)/2+xy for ...

Let `(f(x+y)-f(x))/2 = (f(y)-a)/2+xy` for all real x and y . If f(x) is differentiable and f'(0) exists for all real permissible values of a and is equal to `sqrt(5a-1-a^2)` then f(x) is

A

positive for all real x

B

negative for all real x

C

f(x) = 0 has real roots

D

cannot say anything about the sign of f(x)

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The correct Answer is:
A
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