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Product of all values of t satisfying
4(23t)−39(22t)+54(2t)+16=0
A) 3
B) 1
C) −4
D) −6
Dear Mayank
let 2t =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 2t =2 and 8
or t = 1,3
product =1*3 =3
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