for what value of c are the factor of { x2 -cx + 81/16 } the same ...

Here is answer for your question:

For equal roots 

b2 - 4ac =0

Here b = - c and a = 1 , c = 81/16

Therefore,

b2 – 4ac =0

(-c)2 - 4(1)(81/16) = 0

c2 = 81/16

c = 9/4

Therefore factors are same for c = 9/4 

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