Question

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. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

3

$\tan 30+\tan 15=-b/a=-p$...(i)
$\tan 30\tan 15=c/a=q$...(ii)
$\tan 45=1=\frac{\tan 30+\tan 15}{1-\tan 30\tan 15}$
$=\frac{-p}{1-q}$ after substitution from equation i and ii.
Therefore
$1-q=-p$
$1=q-p$
$q-p+2=1+2=3$
Answer is 3