Complex Numbers And Quadratic Equations question 3
Question: If the two equations $ x^{2}-cx+d=0 $ and $ x^{2}-ax+b=0 $ have one common root and the second has equal roots, then $ 2(b+d)= $
Options:
A) 0
B) $ a+c $
C) $ ac $
D) $ -ac $
Show Answer
Answer:
Correct Answer: C
Solution:
Let roots of $ x^{2}-cx+d=0 $ be $ \alpha ,\beta $ then roots of $ x^{2}-ax+b=0 $ be $ \alpha ,\alpha $ \ $ \alpha +\beta =c,\alpha \beta =d,\alpha +\alpha =a,{{\alpha }^{2}}=b $ Hence $ 2(b+d)=2({{\alpha }^{2}}+\alpha \beta )=2\alpha (\alpha +\beta )=ac $
BETA
