# 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 $$a_{0}+a_{n}$$.