Cubic polynomials

Algebra Level 5

Let \(f (x), g(x)\) be two monic cubic polynomials and \(r\) a real number.

\(f (x)\) has roots \(r+1, r+7\) only.

\(g (x)\) has roots \(r+3, r+9\) only.

Suppose \(f (x)-g (x)=r\) for all \(x\). Find \(r\).

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

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