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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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