logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

Let $f(x)=x^3+3x^2+6x+2009$ and $g(x)=\large\frac{1}{x-f(1)}+\frac{2}{x-f(2)}+\frac{3}{x-f(3)}$.The no of real solutions of $g(x)$=0 is :

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;2&(D)\;\text{infinite}\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
$f'(x)=3x^2+6x+6$
$\Rightarrow 3(x+1)^2+3 > 0\forall x$
$\Rightarrow f(x)$ increases on R
Let $f(1)=a,f(2)=b,f(3)=c$ then $a < b< c$ and
$g(x)=(x-b)(x-c)+2(x-a)(x-c)+3(x-a)(x-c)$
$g(a) >0,g(b)<0$ and $g(c) > 0,g(x)=0$ has exactly two real solution.
Hence (C) is the correct answer.
answered Apr 16, 2014 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...