Complex Numbers And Quadratic Equations question 532
Question: If the roots of the equation $ \frac{\alpha }{x-\alpha }+\frac{\beta }{x-\beta }=1 $ be equal in magnitude but opposite in sign, then $ \alpha +\beta $ =
Options:
A) 0
B) 1
C) 2
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given equation $ \frac{\alpha }{x-\alpha }+\frac{\beta }{x-\beta }=1 $ can be written as Þ $ x^{2}-2(\alpha +\beta )x+3\alpha \beta =0 $ Let roots are $ {\alpha }’ $ and $ -{\alpha }’ $ $ {\alpha }’+(-{\alpha }’)=2(\alpha +\beta )\Rightarrow 0=2(\alpha +\beta )\Rightarrow \alpha +\beta =0 $ .
BETA
