A rational game 4

Algebra Level 4

A polynomial with integer coefficients \(P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}\), with \(a_{n} \) and \(a_{0}\) being positive integers, has one of the roots \(\dfrac{2}{3}\). Find the fourth smallest possible value of \(a_{0}+a_{n}\).


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