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

Let `(f(x+y)-f(x))/2=(f(y)-a)/2+x y` for all real `xa n dydot` If `f(x)` is differentiable and `f^(prime)(0)` exists for all real permissible value of `a` and is equal to `sqrt(5a-1-a^2)dot` Then `f(x)` is positive for all real `x` `f(x)` is negative for all real `x` `f(x)=0` has real roots Nothing can be said about the sign of `f(x)`

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