Decidability of Polynomials with Integer Coefficients and at Least 1 Real Root?

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Homework Statement

Show that the set of polynomials with integer coefficients with at least 1 real root is decidable.

The Attempt at a Solution

The question did not ask for specific language, just an intuitive finite algorithm will do.

 

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In other words, how do you determine whether an integer coefficient polynomial in one variable has at least one real root?

 

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Anyone?

 

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I was thinking maybe by finding the zeros of the derivative, etc, and thus reducing the problem to a recursive one, but I don't know how to do this precisely, or know whether this is the right approach at all.