Y by Adventure10
Let
be the polynomial with leading coefficent 1 and rational coefficents, such that
and with the least degree among all such polynomials. Find
.

![\[p\left(\sqrt{3 + \sqrt{3 + \sqrt{3 + \ldots}}}\right) = 0,\]](http://latex.artofproblemsolving.com/0/f/4/0f472be9f2cede0221e1b4d970d65de94dba01b9.png)

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