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Question 262987: what value of k will make 16x^2/9 (fraction) - kx + 36 a perfect square trinomial?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! what value of k will make 16x^2/9 (fraction) - kx + 36 a perfect square trinomial?
16x^2/9 –kx+36
16x^2 -9kx + 36=0
-9k= 2*4*6
-9k= 48
K= 48/9
16x^2 –9* (48/9) +36=0
16x^2+48x+36=0
(4x+6)^2
Answer by ikleyn(53750)  (Show Source):
You can put this solution on YOUR website! .
what value of k will make 16x^2/9 (fraction) - kx + 36 a perfect square trinomial?
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The post by @mananth gives incorrect answer to the problem's question.
See my solution below for correct, complete and clear solution.
I will give you / (show you) two ways to solve the problem, for your benefits.
S o l u t i o n 1
Your trinomial has a form a^2*x^2 - kx + 36, where a^2 =  , a =  =  .
It will be a complete square if and only if
k = +/-  = +/-  = +/- (2*4*2) = +/- 16. <<<---=== ANSWER
S o l u t i o n 2
Consider the discriminant of the given polynomial
d = " b^2 - 4ac ", where b = -k, a = , c = 36.
So, d = (-k)^2 - 4*(16/9)*36 = k^2 - 16^2.
The given polynomial is a perfect square if and only if the discriminant is zero
k^2 = 16^2, which implies k = +/- 16.
You get the same answer as in Solution 1 above.
Solved correctly and completely, in clear and transparent form.
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