Complex Numbers And Quadratic Equations question 564
Question: If $ \alpha ,\beta $ are the roots of the quadratic equation $ x^{2}+bx-c=0 $ , then the equation whose roots are $ b $ and $ c $ is [Pb. CET 1989]
Options:
A) $ x^{2}+\alpha x-\beta =0 $
B) $ x^{2}-[(\alpha +\beta )+\alpha \beta ]x-\alpha \beta (\alpha +\beta )=0 $
C) $ x^{2}+[(\alpha +\beta )+\alpha \beta ]x+\alpha \beta (\alpha +\beta )=0 $
D) $ x^{2}+[\alpha \beta +(\alpha +\beta )]x-\alpha \beta (\alpha +\beta )=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \alpha +\beta =- $ b and $ \alpha \beta =-c $ Now $ b+c=-[(\alpha +\beta )+\alpha \beta ],bc=(\alpha +\beta )(\alpha \beta ) $ Hence required equation is $ x^{2}+[(\alpha +\beta )+\alpha \beta ]x+\alpha \beta (\alpha +\beta )=0 $ .
BETA
