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# Rational Root Theorem

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.

# Rational Root Theorem

What is the sum of all the rational roots of $x^{7}-2x^{6}+7x-14?$

If a polynomial of degree $$11$$ has integer coefficients, a leading coefficient of $$3$$, and constant term $$11$$, what is the maximum number of distinct rational roots of this polynomial?

What is the sum of the elements of the set $$X=\{3, 11, 26\}$$ that can be roots of the following polynomial for some integers $$m$$ and $$n$$: $x^{6}+mx^{4}+nx-33?$

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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