A) 2
B) \[\frac{1}{3}\]
C) \[\frac{1}{4}\]
D) \[\frac{1}{2}\]
Correct Answer: C
Solution :
For this to represent straight lines \[abc+2fgh-a{{f}^{2}}-b{{g}^{2}}-c{{h}^{2}}=0\] Þ \[{{p}^{2}}+2(-1)\left( \frac{-1}{2} \right)\,\left( \frac{1}{2} \right)-p(1)-1\left( \frac{1}{4} \right)-p\left( \frac{1}{4} \right)\] Þ \[{{p}^{2}}+\frac{1}{2}-p-\frac{1}{4}-\frac{p}{4}=0\]Þ \[{{p}^{2}}-\frac{5p}{4}+\frac{1}{4}=0\] Þ \[4{{p}^{2}}-5p+1=0\] Þ \[4{{p}^{2}}-4p-p+1=0\] Þ \[(4p-1)(p-1)=0\] Þ \[p=\frac{1}{4},\,1.\]
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