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The rational root theorem describes a relationship between the roots of a polynomial and its coefficients. For a good time, use the theorem to prove that the square root of 2 is not rational.

What is the sum of all the rational roots of \( x^3 - 9x^2 + 3x -27 =0 \)?

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What is the sum of the rational roots of \(f(x) = x^3 - 6x^2 + 18x -65\)?

**Details and assumptions**

You may choose to read the blog post on the rational root theorem.

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