Algebra

# Rational Root Theorem - Polynomial Zeros

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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