1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook