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
by
Joel Tan