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Need a little help with biquadratic equations

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data

    Ok, so here's the problem:
    Prove, that biquadratic equation's x4+px2+q=0 sum of all solutions is equal to zero, and product is equal to q.

    2. Relevant equations



    3. The attempt at a solution
    I don't really know how to solve it so I'd be very grateful if someone could help me. Thank you
     
  2. jcsd
  3. Mar 17, 2009 #2

    Mark44

    Staff: Mentor

    This equation is quadratic in form, which you can see by letting u = x2. This makes the new equation u2 +pu + q = 0.
    Solve that equation for u by using the quadratic formula, getting two values of u.
    Replace u by x2, getting four values of x.
     
  4. Mar 17, 2009 #3
    While that equation is quadratic in form, for the purpose of the question think of it as x4+ 0*x3+ px2 +0*x+q=0. Do you know any general ways to relate the coefficients of a polynomial with the roots? If you're having trouble try multiplying out (x-a)(x-b)(x-c)(x-d)=0. That will become a polynomial with roots equal to a,b,c, and d.
     
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