Complex Numbers And Quadratic Equations question 550
Question: If the sum of the roots of the equation $ x^{2}+px+q=0 $ is three times their difference, then which one of the following is true [Dhanbad Engg. 1968]
Options:
A) $ 9p^{2}=2q $
B) $ 2q^{2}=9p $
C) $ 2p^{2}=9q $
D) $ 9q^{2}=2p $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ \alpha ,\beta $ are roots of $ x^{2}+px+q=0 $ So $ \alpha +\beta =-p $ and $ \alpha \beta =q $ Given that $ (\alpha +\beta )=3(\alpha -\beta )=-p $
Þ $ \alpha -\beta =\frac{-p}{3} $ Now $ {{(\alpha -\beta )}^{2}}={{(\alpha +\beta )}^{2}}-4\alpha \beta $
Þ $ \frac{p^{2}}{9}=p^{2}-4q $ or $ 2p^{2}=9q $ .
BETA
