Complex Numbers And Quadratic Equations question 741
Question: The number of solutions of $ \frac{\log 5+\log (x^{2}+1)}{\log (x-2)}=2 $ is
Options:
A) 2
B) 3
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ \frac{\log 5+\log (x^{2}+1)}{\log (x-2)}=2 $
Þ $ \log {5(x^{2}+1)}=\log {{(x-2)}^{2}}\Rightarrow 5(x^{2}+1)={{(x-2)}^{2}} $
$ \Rightarrow $ $ 4x^{2}+4x+1=0\Rightarrow x=-\frac{1}{2} $ But for $ x=-\frac{1}{2}\log (x-2) $ is not meaningful. Hence it has no root.
BETA
