Complex Numbers And Quadratic Equations question 538
Question: If $ \alpha ,\beta $ are the roots of $ (x-a)(x-b)=c, $ $ c\ne 0, $ then the roots of $ (x-\alpha )(x-\beta )+c=0 $ shall be [IIT 1992; MP PET 2000; DCE 2000]
Options:
A) a, c
B) $ b,c $
C) $ a,b $
D) $ a+c,b+c $
Show Answer
Answer:
Correct Answer: C
Solution:
As given, $ \alpha +\beta =a+b $ , $ \alpha \beta =ab-c $ or $ ab=\alpha \beta +c $ . Then the required equation is $ x^{2}-x(\alpha +\beta )+\alpha \beta +c=0 $ $ \Leftrightarrow x^{2}-x(a+b)+ab=0 $ , whose roots are a, b.
BETA
