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If a is a constant such that \(9x^2 + 24x + a\) is the square of a binomial, then what is a?

 Apr 15, 2020
 #1
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a is 16, since the binomial is of form (3x+4)^2 since 3^2=9 and 3*4*2=24. 4^2=16 im sorry that this isnt clear or if it's wrong.

 Apr 15, 2020
 #2
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9x^2 + 24x + a =

9 (x^2 + 24/9 x + a/9)        'complete the square'

     9(x^2 + 24/9x  + 144/81)      where 144/81 = a/9       a = 16

 

      9 ( x + 12/9)^2

        9 x^2 + 24x + 16  =

(3x+4)^2              

 Apr 15, 2020
 #3
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this is so much more clear than my solution, thanks!

Guest Apr 15, 2020
 #4
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Thank you so much!

 

-OP

Guest Apr 15, 2020

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