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A perfect square trinomial stumped.

  1. Feb 6, 2006 #1
    ok, I'm pretty sure this is ridiculously simple, but I am stumped by this question..

    What value of k would make 25x^2 - 60xy + ky^2 a perfect square trinomial?

    I just don't know where to begin in order to find k. :uhh:

    Any help would be much appreciated!
  2. jcsd
  3. Feb 6, 2006 #2
    Ok well starting with a binomial (A + B)
    then (A + B)2 = (A + B)(A + B) = A2 + AB + AB + B2

    which is the same as

    A2 + 2AB + B2

    Which would be a perfect square trinomial so do you think you could right the trinomial in question in this form for some value of k?
  4. Feb 6, 2006 #3


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    Just a tiny bit more help: as d leet said, a perfect square must be of the form (A+ B)2= A2+ 2AB+ B2.
    Your formula is 25x2- 60xy+ ky2. That means you must have A2= 25x2, 2AB= -60xy and B2= ky2. From the first equation it should be obvious what A. Use that in the second equation to determine B and then use the third equation to find k.
  5. Feb 6, 2006 #4
    Easy method - This is a perfect square. So discriminant must be 0. Put y = 1, so that this becomes a quadratic in x if you don't understand to usewhat I am talking about in the first statement. And I don't think this is a bad method.
    So you would get 60^2 = 4*25*k.
    Moreover here the value of y does not matter if you look deep. The co-efficient of first power of x is 60y and the constant is ky^2
    So (60y)^2 = 4*25*k*y^2.
  6. Feb 6, 2006 #5
    Ah! Thank You Guys! I see how it works now! :rolleyes:
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