Cubic polynomials

Algebra Level 5

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

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

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

Suppose f(x)g(x)=rf (x)-g (x)=r for all xx. Find rr.

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

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