Algebra

Rational Root Theorem

Rational Root Theorem

         

What is the sum of all the rational roots of x72x6+7x14?x^{7}-2x^{6}+7x-14?

If a polynomial of degree 1111 has integer coefficients, a leading coefficient of 33, and constant term 1111, 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}X=\{3, 11, 26\} that can be roots of the following polynomial for some integers mm and nn: x6+mx4+nx33?x^{6}+mx^{4}+nx-33?

What is the product of all the distinct rational roots of the polynomial 2x39x2+12x4?2x^3-9x^2+12x-4?

What is the sum of all real roots of the polynomial x3+2x2+2x51?x^3+2x^2+2x-51?

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