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)   (Show Source): You can put this solution on YOUR website!
Setting the discriminant equal to 0 and simplifying gives you , which appears factorable.
Answer by greenestamps(13198)   (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



the roots are given by the quadratic formula,



The radicand 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.



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



So the trinomial is a perfect square if the discriminant is 0:




or

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

CHECK:
k=5:
k=-1:


Answer by MathTherapy(10551)   (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..

      <==== Standard form of a quadratic
By EQUATING terms, we see that: 
                                +  +    =  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:

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