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What value of k will make \(4x^2 - 20x + k\) the square of a binomial?

 Dec 31, 2017
 #1
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4x^2  -  20x  +  k

 

We want  something like this :

 

(2x  - √k) (2x - √k)  =   4x^2  -   2√kx - 2√kx  + k  = 4x^2 - 4√kx  +  k

 

So....it appears that.we need to have   

 

-20  =   -4√k           square both sides

 

400  =  16k             divide both sides by 16

 

25  =  k

 

Proof

 

(2x  - √25) (2x - √25)  = 

(2x - 5)(2x - 5)  = 

(2x - 5)^2  =

4x^2 - 10x - 10x  + 25  = 

4x^2 - 20x + 25

 

So  the  binomial  is just   (2x  - 5)

 

 

 

cool cool cool

 Dec 31, 2017
edited by CPhill  Dec 31, 2017

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