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Roots of polynomials

  1. Jul 3, 2010 #1
    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)[tex]\in[/tex]Q[x], p[tex]\neq[/tex]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. jcsd
  3. Jul 3, 2010 #2
    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.
     
  4. Jul 3, 2010 #3
    Thank you for the advice. I will use it.
     
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