Find degree of polynomial satisfying given condition – math.stackexchange.com

Find degree of polynomial satisfying given condition – math.stackexchange.com

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Question: If $f(x)$ is a polynomial of degree $n$ such that $$1+f(x)=\frac{f(x-1)+f(x+1)}{2} \forall x\in R$$ then find $n$. My attempt: I first started off by trying to prove $f(x)$ to be ...

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