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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.

How many rational roots does \({ x }^{ 1000 }-{ x }^{ 500 }+{ x }^{ 100 }+x+1=0\) have?

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Find the sum of all real roots of

\[\ 27x^3+21x+8 = 0\]

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