Finding the Perfect Value of k for a Square Trinomial: A Step-by-Step Guide

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In summary, this question is ridiculously simple, but I am stumped by this value of k. Any help would be much appreciated!
  • #1
soggybread
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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!
 
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  • #2
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
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
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
Ah! Thank You Guys! I see how it works now! :rolleyes:
 

What is a perfect square trinomial?

A perfect square trinomial is a polynomial expression of degree two that can be factored into the square of a binomial. It follows the format of a2 + 2ab + b2.

How can you identify if a trinomial is a perfect square?

To identify a perfect square trinomial, you can check if the first and last terms are perfect squares and if the middle term is twice the product of the square roots of the first and last terms.

What is the factored form of a perfect square trinomial?

The factored form of a perfect square trinomial is (a + b)2, where a and b are the square roots of the first and last terms, respectively.

How do you solve equations involving perfect square trinomials?

To solve equations involving perfect square trinomials, you can either use the factored form or complete the square. Completing the square involves adding and subtracting a constant term to both sides of the equation to make it a perfect square trinomial.

What are some real-life applications of perfect square trinomials?

Perfect square trinomials are commonly used in physics and engineering to model the motion of objects under constant acceleration. They are also used in geometry to solve problems related to area and volume, as well as in financial calculations involving compound interest.

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