For the record, $$2$$ and $$-3$$ are two roots. The last two roots can easily be found from the remaining quadratic equation. $$-3$$ can be discarded due to being a negative number whereas a root is always positive. As for the two roots from the quadratic equation, one is negative, whereas the other one is larger than $$\sqrt{7}$$ which is in contradiction with the initial root problem, so both can be discarded too. Only $$2$$ is a valid solution to the initial problem.

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[Not-so-daily puzzle] Nested roots

You can use [Polynomial long division](https://en.wikipedia.org/wiki/Polynomial_long_division) to find the factors of this quartic equation...

But guessing in this case works too, and is faster :)