Problem

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Tags: algebra, Polynomials, polynomial



Let $f(x)$ be a polynomial with real coefficients of degree 2. Suppose that for some pairwise distinct real numbers , $a,b,c$ we have: \[f(a)=bc , f(b)=ac, f(c)=ab\]Dertermine $f(a+b+c)$ in terms of $a,b,c$.