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What is the sum of all possible values of for which x^2 + kx - 10x + 36 is the square of a binomial?

 Jul 17, 2021
edited by Guest  Jul 17, 2021
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What is the sum of all possible values of for which x^2 + kx - 10x + 36 is the square of a binomial?   

 

For the square of the binomial to end with +36, the binomial must be either (x + 6)2 or (x – 6)2

So (kx – 10x) has to equal either +12x or –12x. 

 

If (kx – 10x) equals +12x, then k is +22. 

If (kx – 10x) equals –12x, then k is –2. 

 

The sum of +22 and –2 is 20.  

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 Jul 18, 2021

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