A) 2
B) 3
C) 0
D) 1
Correct Answer: B
Solution :
Given equation is \[{{x}^{2}}+px+q=0\] |
Sum of roots \[=\tan 30{}^\circ +\tan 15{}^\circ =-p\] |
Product of roots \[=\tan 30{}^\circ .\tan 15{}^\circ =q\] |
\[\tan 45{}^\circ =\frac{\tan 30{}^\circ +\tan 15{}^\circ }{1-\tan 30{}^\circ .\tan 15{}^\circ }=\frac{-p}{1-q}=1\] |
\[\Rightarrow \,\,\,-p=1-q\,\,\Rightarrow \,q-p=1\] |
\[\therefore \,\,2+q-p=3\] |
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