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What is the sum of all possible values of k for which \(x^2 + kx - 9x + 25\) is the square of a binomial?

 

Can you please give me steps or answer if possible? 

 Jun 15, 2021

Best Answer 

 #1
avatar+33757 
+2

(k-9)    = a+b        and     a*b = 25           factors of 25 :        5  5      25  1      -5   -5        -25   -1        (these are   'a' and 'b')

                                                                          since we want a square of a binomial.....only the RED pairs above apply ....

Taking each one :

k-9  = 5+5

k = 19                                  binomial is   (x+5)^2   = x^2 + 10x + 25

 

Can you do the other?                      

 Jun 15, 2021
 #1
avatar+33757 
+2
Best Answer

(k-9)    = a+b        and     a*b = 25           factors of 25 :        5  5      25  1      -5   -5        -25   -1        (these are   'a' and 'b')

                                                                          since we want a square of a binomial.....only the RED pairs above apply ....

Taking each one :

k-9  = 5+5

k = 19                                  binomial is   (x+5)^2   = x^2 + 10x + 25

 

Can you do the other?                      

ElectricPavlov Jun 15, 2021

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