# Cubic polynomials II

Algebra Level 5

Suppose two polynomials of degree 3, $$f(x), g(x)$$ have three distinct positive integer roots each, and there is no common root between both polynomials. (In other words, the set of roots of these polynomials has 6 distinct elements.)

Also, $$f(x)-g(x)=r$$ for some real number $$r$$ for all real values of $$x$$.

If $$S(P(x))$$ denotes the sum of absolute values of coefficients of a polynomial $$P(x)$$, find the minimum possible value of $$S(f(x))+S(g(x))$$.

This problem is part of the set ... and polynomials

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