Complex Numbers And Quadratic Equations question 603
Question: If A.M. of the roots of a quadratic equation is 8/5 and A.M. of their reciprocals is 8/7, then the equation is [AMU 2001]
Options:
A) $ 5x^{2}-16x+7 $ = 0
B) $ 7x^{2}-16x+5=0 $
C) $ 7x^{2}-16x+8=0 $
D) $ 3x^{2}-12x+7=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the roots are a and b
$ \Rightarrow \frac{\alpha +\beta }{2}=\frac{8}{5} $
$ \Rightarrow \alpha +\beta =\frac{16}{5} $ …….(i) and $ \frac{\frac{1}{\alpha }+\frac{1}{\beta }}{2}=\frac{8}{7} $
$ \Rightarrow \frac{\alpha +\beta }{2\alpha \beta }=\frac{8}{7} $
$ \Rightarrow \frac{(16/5)}{2(8/7)}=\alpha \beta $
$ \Rightarrow \alpha \beta =\frac{7}{5} $ …….(ii) \ Equation is $ x^{2}-( \frac{16}{5} )x+\frac{7}{5}=0 $
$ \Rightarrow 5x^{2}-16x+7=0 $ .
BETA
