Ask Questions, Get Answers

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

Sum of rational roots of $x^5=\large\frac{133x-78}{133-78x}$ is

$\begin{array}{1 1}(A)\;\large\frac{2}{9}&(B)\;\large\frac{9}{2}\\(C)\;\large\frac{6}{13}&(D)\;\large\frac{13}{6}\end{array} $

Can you answer this question?

1 Answer

0 votes
$\Rightarrow 78x^6-133x^5+133x-78=0$
$x=1,-1$ are roots
Dividing by $(x^2-1)$ we get
Dividing by $x^2$ we get
$\Rightarrow 78(x^2+\large\frac{1}{x^2})$$-133(x+\large\frac{1}{x})$$+78=0$
Putting $x+\large\frac{1}{x}$$=y$ we get
$\Rightarrow y=\large\frac{13}{6},-\frac{6}{13}$
$\Rightarrow x+\large\frac{1}{x}=\frac{13}{6}$
$\Rightarrow x=\large\frac{2}{3},\frac{3}{2}$
$\Rightarrow$ Gives imaginary roots
Hence rational roots are $1,-1,\large\frac{2}{3},\frac{3}{2}$
Sum of rational roots =$\large\frac{13}{6}$
Hence (D) is the correct answer.
answered Apr 16, 2014 by sreemathi.v

Related questions

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