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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```
7 years ago

147 Points
```										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
Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin
```
7 years ago
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