If ,\tan30^\circ and \tan15^\circ are the roots of the equation x^{2}+px+q=0 then 2+q-p=

AP ICET 2017 Shift 1 Paper

Question : 119 of 200

Marks: +1, -0

,\tan30°

and

\tan15°

are the roots of the equation

x^{2}+px+q=0

then

2+q-p=

Solution:

x^2+px+q=0

Sum of roots :

\tan30°+\tan15°=-p

product of roots :

\tan30°.\tan15°=q

∴q-p=\tan30°.\tan15°+\tan30°+\tan15°

={1}/{√{3}}({√{3}-1}/{√{3}+1})+{1}/{√{3}}+({√{3}-1}/{√{3}+1})

={√{3}-1+√{3}+1+3-√{3}}/{√{3}(√{3}+1)}={√{3}+3}/{3+√{3}}=1

∴2+q-p=2+1=3

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