Complex Numbers And Quadratic Equations question 31
Question: If a and b (a < b) are the roots of the equation $ x^{2}+bx+c=0, $ where $ c<0<b, $ then [IIT Screening 2000; Pb. CET 2000]
Options:
A) $ 0<\alpha <\beta $
B) $ \alpha <0<\beta <|\alpha | $
C) $ \alpha <\beta <0 $
D) $ \alpha <0<|\alpha |<\beta $
Show Answer
Answer:
Correct Answer: B
Solution:
Here $ D=b^{2}-4c>0 $ because c < 0 < b. So roots are real and unequal. Now, $ \alpha +\beta =-b<0 $ and $ \alpha \beta =c<0 $ \ One root is positive and the other negative, the negative root being numerically bigger. As $ \alpha <\beta ,\alpha $ is the negative root while b is the positive root. So, $ |\alpha |>\beta and\alpha <0<\beta . $
BETA
