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Determinants question

  1. Dec 31, 2004 #1
    Hi, I' not sure if I've done this question correctly so I just want someone to tell me where I've gone wrong (if I have).

    Evaluate the following determinant as a product of two terms. Hence find, in terms of p the values of x for which it vanishes.

    Grr, I can't seem to use LaTeX properly so I'll just "draw" the determinant:

    x x 0
    0 x p
    -2x -p x

    [tex]= x \left\vert \begin{array}{cc} x & p\\-p & x \end{array}\right\vert - x \left\vert \begin{array}{cc} 0 & p\\-2x & x \end{array}\right\vert[/tex]

    = x(x^2 + p^2) - x(2xp)
    =x^3 + p^2.x - 2x^2.p
    - x(x^2 - 2px + p^2) = 0

    x = {-(-2p) +- [(-2p)^2 - 4.1.p^2]^1/2}/2

    x = [2p +- (4p^2 - 4p^2)^1/2]/2

    x = p

    It doesn't look right to me :/.
    Last edited: Dec 31, 2004
  2. jcsd
  3. Dec 31, 2004 #2
    This is correct x(x-p)^2=0
    ==>x=0 or x=p
  4. Dec 31, 2004 #3
    LOL, can't believe I didn't see that :redface:. Thanks a lot :smile:.
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