Complex Numbers And Quadratic Equations question 553
Question: If the roots of the equation $ ax^{2}+bx+c=0 $ are $ l $ and $ 2l $ , then [MP PET 1986; MP PET 2002]
Options:
A) $ b^{2}=9ac $
B) $ 2b^{2}=9ac $
C) $ b^{2}=-4ac $
D) $ a^{2}=c^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ l+2l=-\frac{b}{a}\Rightarrow l=-\frac{b}{3a} $ …..(i) and $ l.2l=\frac{c}{a} $
Þ $ l^{2}=\frac{c}{2a} $
Þ $ {{( -\frac{b}{3a} )}^{2}}=\frac{c}{2a}\Rightarrow \frac{b^{2}}{9a^{2}}=\frac{c}{2a} $ or $ 2b^{2}=9ac $ Aliter: Obviously ratio of roots is 1 : 2, so applying $ mnb^{2}={{(m+n)}^{2}}ac $
Þ $ 2b^{2}=9ac $ .
BETA
