JEE Main & Advanced Sample Paper JEE Main - Mock Test - 7

If the roots of the quadratic equation \[{{x}^{2}}+px+q=0\] are \[\tan 30{}^\circ \] and \[\tan 15{}^\circ \] respectively, then the value of \[2+q-p\]is

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 \[=\tan 30{}^\circ .\tan 15{}^\circ =q\]

\[\tan 45{}^\circ =\frac{\tan 30{}^\circ +\tan 15{}^\circ }{1-\tan 30{}^\circ .\tan 15{}^\circ }=\frac{-p}{1-q}=1\]

\[\Rightarrow \,\,\,-p=1-q\,\,\Rightarrow \,q-p=1\]

\[\therefore \,\,2+q-p=3\]