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 \[=\tan 30{}^\circ .\tan 15{}^\circ =q\] \[\tan 45{}^\circ =\frac{\tan 30{}^\circ +\tan 15{}^\circ }{1-\tan 30{}^\circ .\tan 15{}^\circ }=\frac{-p}{1-q}=1\] \[\Rightarrow \,\,\,-p=1-q\,\,\,\,\Rightarrow \,\,\,q-p=1\] \[\therefore \,\,\,2+q-p=3\]You need to login to perform this action.
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