# Rationality of roots of polynomial equations

what's the rationality of the roots of polynomial related to the rationality of its coefficient? Here is the question just came up to me, is that true for a polynomial with irrational coefficient cannot has a rational root. Is any theorem about this?

-
Hint $\rm\ \pi x\$ has a rational root. –  Math Gems Mar 3 '13 at 18:14

As another example, the polynomial $$x^2 - (\pi +1) x + \pi$$ has $1$ as a root, and no multiple of it by a nonzero constant has all coefficients rational.
If you want all coefficients to be non-rational, (see comment by @MartinBrandenburg) $$\pi x^2 - (\pi^2 +\pi) x + \pi^2$$ will do.