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Let f(x) = 2x + 1, then the number of real values of x for which the three unequal numbers f(x),f(2x), f(4x) are in geometric progression is

Let f(x) = 2x + 1, then the number of real values of x for which the three unequal numbers f(x),f(2x), f(4x) are in geometric progression is

Grade:11

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
5 years ago
Hii

Find out the values of the function and you will get the relation if you apply property of GM on the three given terms.
Divya Nitin Nikhade
13 Points
2 years ago
(f(2x))power 2=(fx).(f(4x)) .                                            2(2x+1)power 2=(2x+1).(2(4x)+1) .                             (4x+1)power 2=(2x+1).(8x+1) .                                     16x power 2+1+8x=16xpower2+10x+1 .                     8x=10x .                                                                           10x-8x=0 .                                                                          2x=0 .                                                                               x=0

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