Complex Numbers And Quadratic Equations question 609
Question: If the roots of the equation $ 12x^{2}-mx+5=0 $ are in the ratio 2 : 3, then m = [RPET 2002]
Options:
A) $ 5\sqrt{10} $
B) $ 3\sqrt{10} $
C) $ 2\sqrt{10} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let roots area, b so, $ \frac{\alpha }{\beta }=\frac{2}{3}\Rightarrow \alpha =\frac{2\beta }{3} $ \ $ \alpha +\beta =\frac{m}{12} $
Þ $ \frac{2\beta }{3}+\beta =\frac{m}{12}\Rightarrow \frac{5\beta }{3}=\frac{m}{12} $ …….(i) and $ \alpha \beta =\frac{5}{12}\Rightarrow \frac{2\beta }{3}.\beta =\frac{5}{12}\Rightarrow {{\beta }^{2}}=\frac{5}{8} $
$ \Rightarrow \beta =\sqrt{5/8} $ Put the value of b in (i), $ \frac{5}{3}.\sqrt{\frac{5}{8}}=\frac{m}{12} $
Þ $ m=5\sqrt{10} $ .
BETA
