Product of all values of t satisfying4(23t)−39(22t)+54(2t)+16=0A) 3B) 1C) −4D) −6

Dear Mayank

let   2^t =x  ( x is always positive)

so equation become  4(x³)−39(x²)+54(x)+16=0

   clearly x=2 is its solution

so (x-2) is its one factor

let other 2 roots are a and b

  a+b+2 =39/4    or  a+b =31/4

  a.b.2 =-16/4

  a.b =-2

 solve for a and b 

 a =8  and b=-1/4

 b root is not possible because x is positive

so 2^t =2 and 8

 or  t = 1,3

product =1*3 =3

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