logo

Ask Questions, Get Answers

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

Roots of the equation $12x^2+mx+5=0$ are in the ratio $3 : 2$,then $m$ equals

$\begin{array}{1 1}(A)\;\large\frac{5}{12}&(B)\;\large\frac{1}{12}\\(C)\;\large\frac{5\sqrt{10}}{12}&(D)\;5\sqrt{10}\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Let the roots be $\alpha,\beta$
$\large\frac{\alpha}{\beta}=\frac{3}{2}$
$\alpha+\beta=-\large\frac{m}{12}$
$\alpha\beta=\large\frac{5}{12}$
$\alpha=\large\frac{3}{2}$$\beta\Rightarrow\large\frac{3}{2}$$\beta^2=\large\frac{5}{12} $
$\Rightarrow \beta^2=\large\frac{10}{36}\Rightarrow \beta=-\large\frac{\sqrt{10}}{6}$
$\alpha=\large\frac{3}{2}$$\beta=-\large\frac{\sqrt{10}}{4}$
$m=-12(\alpha+\beta)$
$\;\;\;=12(\large\frac{\sqrt{10}}{6}+\frac{\sqrt{10}}{4})$
$\;\;\;=5\sqrt{10}$
Hence (D) is the correct answer.
answered Apr 14, 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
...