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

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Homework Help Overview

The discussion revolves around the decidability of polynomials with integer coefficients that have at least one real root, focusing on the methods to determine this property.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore how to determine if a polynomial with integer coefficients has a real root, with some considering the role of the derivative in finding zeros.

Discussion Status

The discussion is ongoing, with participants sharing initial thoughts and approaches without reaching a consensus. Some guidance on potential methods has been suggested, but clarity on the exact approach remains elusive.

Contextual Notes

The original poster notes that the problem does not specify a particular programming language, indicating a focus on an intuitive finite algorithm.

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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?
 
Anyone?
 
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.
 

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