SOLUTION: The positive value of k which will make 4x2 - 4kx + 4k + 5 = 0 a perfect square trinomial is _____. -- Please help me..

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Question 1182830: The positive value of k which will make
4x2 - 4kx + 4k + 5 = 0 a perfect square trinomial is _____.

-- Please help me..
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Setting the discriminant equal to 0 and simplifying gives you k%5E2-4k-5=0, which appears factorable.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


It appears to me that the response from the other tutor is only useful for a student who already knows how to solve the problem.

Assuming you posted the question because you don't know how to solve the problem, I will provide a response that I hope will help you learn how.

For the general quadratic equation

y+=+ax%5E2%2Bbx%2Bc

the roots are given by the quadratic formula,

%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a

The radicand b%5E2-4ac is the discriminant -- it tells whether the equation has 0, 1, or 2 real zeros (roots). If the discriminant is 0, then the equation has a single root; that means the quadratic is a perfect square trinomial.

So you need the discriminant of the given trinomial to be 0.

y+=+%284%29x%5E2+%2B+%28-4k%29x+%2B+%284k%2B5%29

In this trinomial, a=4, b=-4k, and c=4k+5. The discriminant is

b%5E2-4ac+=+%28-4k%29%5E2-4%284%29%284k%2B5%29+=+16k%5E2-64k-80

So the trinomial is a perfect square if the discriminant 16k%5E2-64k-80 is 0:

16k%5E2-64k-80=0
k%5E2-4k-5=0
%28k-5%29%28k%2B1%29=0
k=5 or k=-1

ANSWER: the trinomial is a perfect square if k is either 5 or -1.

CHECK:
k=5: 4x%5E2-20x%2B25+=+%282x-5%29%5E2
k=-1: 4x%5E2-4k%2B1+=+%282x-1%29%5E2

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
The positive value of k which will make
4x2 - 4kx + 4k + 5 = 0 a perfect square trinomial is _____.

-- Please help me..
matrix%281%2C3%2C+4x%5E2+-+4kx+%2B+4k+%2B+5%2C+%22=%22%2C+0%29
     matrix%281%2C3%2C+ax%5E2+%2B+bx+%2B+c%2C+%22=%22%2C+0%29 <==== Standard form of a quadratic
By EQUATING terms, we see that: 
                                highlight%28a%29x%5E2+  highlight%28b%29x+  highlight%28c%29  =  0
              Therefore, we get: a = 4
                                 b = - 4k
                                 c = + 4k + 5 

                                  
In order for the polynomial to be a PERFECT SQAURE, the discriminant (b2 - 4ac) MUST = 0. 
                    We then get: 
                                        (k - 5)(k + 1) = 0
                                    k - 5 = 0    OR      k + 1 = 0
                                        k = 5    OR         k = - 1

Since a  POSITIVE value for k is required, the ONLY ANSWER is: highlight_green%28matrix%281%2C3%2C+k%2C+%22=%22%2C+5%29%29