Roots of Polynomials: Finding g(y) with y1, y2, y3

[mattewmath]

Homework Statement

Let x₁, x₂, x₃ are the roots of the polynomial f(x)=x³+px+q, where f(x)\inQ[x], p\neq0. Find a polynomial g(y) of third degree with roots:

y₁=x₁/(x₂+x₃-q)
y₂=x₂/(x₁+x₃-q)
y₃=x₃/(x₁+x₂-q)

Homework Equations

The Attempt at a Solution

Any ideas? Thank you.

 

[Unit]

Not guaranteeing a solution, but recall that a polynomial with roots can always be factored into the form y = (x - r₁)(x - r₂)(x - r₃) where r_n is a unique root. Try this with your three roots.

 

[mattewmath]

Thank you for the advice. I will use it.