# Roots of polynomials

1. Jul 3, 2010

### mattewmath

1. The problem statement, all variables and given/known data

Let x1, x2, x3 are the roots of the polynomial f(x)=x3+px+q, where f(x)$$\in$$Q[x], p$$\neq$$0. 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)

2. Relevant equations

3. The attempt at a solution

Any ideas? Thank you.

2. Jul 3, 2010

### 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 rn is a unique root. Try this with your three roots.

3. Jul 3, 2010

### mattewmath

Thank you for the advice. I will use it.