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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 - Polynomials

         

What is the sum of all the rational roots of \( x^3 - 9x^2 + 3x -27 =0 \)?

If \(a\) is the sum of all real roots of the polynomial \[7x^3+6x^2+20x-3,\] what is the value of \(245a\)?

If \(a\) is the sum of all real roots of the polynomial \[7x^3-8x^2+15x-2,\] what is the value of \(161a\)?

\(f(x) = 16 x^3 - 33 x^2 + 16 x - 33\). The real root of \(f(x)\) has the form \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

What is the sum of the rational roots of \(f(x) = x^3 - 6x^2 + 18x -65\)?

Details and assumptions

You may choose to read the blog post on the rational root theorem.

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