A) \[{{b}^{2}}=9ac\]
B) \[2{{b}^{2}}=9ac\]
C) \[{{b}^{2}}=-4ac\]
D) \[{{a}^{2}}={{c}^{2}}\]
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 \[{{\left( -\frac{b}{3a} \right)}^{2}}=\frac{c}{2a}\Rightarrow \frac{{{b}^{2}}}{9{{a}^{2}}}=\frac{c}{2a}\]or \[2{{b}^{2}}=9ac\] Aliter: Obviously ratio of roots is 1 : 2, so applying \[mn{{b}^{2}}={{(m+n)}^{2}}ac\] Þ \[2{{b}^{2}}=9ac\].
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