KVPY Sample Paper KVPY Stream-SX Model Paper-23

The number of solution of the equation \[\log \,(-2x)=2\log \,(x+1)\] is

A) 0

B) 1

C) 2

D) 3

Correct Answer: B

Solution :

We have,\[\log \,(-2x)=2\log \,(x+1)\]

\[-2x>0x<0\]and \[x+1>0x>-\,1\]

\[\therefore \]\[x\in \,(-1,0)\]

\[-2\,x={{(x+1)}^{2}}\]\[\Rightarrow \]\[{{x}^{2}}+4x+1=0\]\[\Rightarrow \]\[x=\frac{-\,4\pm 2\sqrt{3}}{2}=-2\pm \sqrt{3}\]

So, \[x=-\,2+\sqrt{3}\]only one solution lies in \[(-1,0).\]