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Two poles, \( \mathrm{AB} \) of length a metres and \( \mathrm{CD} \) of length \( \mathrm{a}+\mathrm{b} \) metres \( (\mathrm{a} \neq \mathrm{b}) \) are exected at same horizontal level
P with bases at \( \mathrm{B} \) and \( \mathrm{D} \). If \( \mathrm{BD}=x \) and \( \tan \angle \mathrm{ACB}=\frac{1}{2} \), then,
[JEE Mains-2021 (August)]
(a) \( x^{2}+2(\mathrm{a}+2 \mathrm{~b}) x-\mathrm{b}(\mathrm{a}+\mathrm{b})=0 \)
(b) \( x^{2}+2(\mathrm{a}+2 \mathrm{~b}) x+\mathrm{a}(\mathrm{a}+\mathrm{b})=0 \)
(c) \( x^{2}-2 a x+b(a+b)=0 \)
(d) \( x^{2}-2 a x+a(a+b)=0 \)
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