Finding the Perfect Value of k for a Square Trinomial

[soggybread]

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.

Any help would be much appreciated!

 

[d_leet]

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.

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?

 

[HallsofIvy]

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= 25x^{2, 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.}

 

[vaishakh]

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.

 

[soggybread]

Ah! Thank You Guys! I see how it works now!