Proving Rational Roots and Irrationality of \sqrt{2}

[Edelman]

Homework Statement

Prove that a rational root of a monic polynomial is an integer. Use this to prove that the $\sqrt{2}$ is irrational.

Homework Equations

The Attempt at a Solution

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I am really not sure where to begin?

 

[Office_Shredder]

What about the polynomial x-1/2? It seems like there are some conditions missing from your problem statement. I'm guessing that your polynomial is supposed to have integer coefficients - if you start with the case when the polynomial is a quadratic, once you figure that out it should be clear how to proceed with the general case