Question

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

• A. $3$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (A)

Since tan $30^°$ and $tan\, 15^°$ are roots of equation $x^2+px+q=0.$
$\therefore tan\,30^{°}+tan\,15^{°}=- p$
and $tan\,30^{°}\,tan\,15^{°}=q$
Therefore
$2+q-p=2+tan\,30^{°}\,tan\,15^{°} +\left(tan\,30^{°}\right)$
$=2+tan\,30^{°}\,tan\,15^{°}+1-tan\,30^{°}\,tan\,15^{°}$
$\left(\because tan\,45^{°}=\frac{tan\,30^{°}+tan\,15^{°}}{1-tan\,30^{°}\,tan\,15^{°}}\right)$
$\Rightarrow 2+q-p=3$