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A perfect square trinomial stumped.

  • Thread starter soggybread
  • Start date
  • #1
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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!
 

Answers and Replies

  • #2
1,074
1
soggybread said:
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!
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?
 
  • #3
HallsofIvy
Science Advisor
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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.
 
  • #4
335
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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.
 
  • #5
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Ah! Thank You Guys! I see how it works now! :rolleyes:
 

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