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 \[x^{7}-2x^{6}+7x-14?\]

What is the product of all the distinct rational roots of the polynomial \[2x^3-9x^2+12x-4?\]

What is the sum of all real roots of the polynomial \[x^3+2x^2+2x-51?\]

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