Complex Numbers And Quadratic Equations question 527
Question: If $ \alpha $ and $ \beta $ are the roots of the equation $ x^{2}-a(x+1)-b=0 $ then $ (\alpha +1)(\beta +1)= $
Options:
A) b
B) - b
C) $ 1-b $
D) $ b-1 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation $ x^{2}-a(x+1)-b=0 $
Þ $ x^{2}-ax-a-b=0 $
Þ $ \alpha +\beta =a,\alpha \beta =-(a+b) $ Now $ (\alpha +1)(\beta +1)=\alpha \beta +\alpha +\beta +1 $ = $ -(a+b)+a+1=1-b $
BETA
