Complex Numbers And Quadratic Equations question 611
Question: The condition that one root of the equation $ ax^{2}+bx+c=0 $ is three times the other is [DCE 2002]
Options:
A) $ b^{2}=8ac $
B) $ 3b^{2}+16ac=0 $
C) $ 3b^{2}=16ac $
D) $ b^{2}+3ac=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let the roots are a and 3a \ $ \alpha +3\alpha =\frac{-b}{a}\Rightarrow \alpha =-\frac{b}{4a} $ and $ \alpha .3\alpha =\frac{c}{a} $
Þ $ \frac{c}{a}=3.\frac{b^{2}}{16a^{2}} $
Þ $ 16ac=3b^{2} $ .
BETA
