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°
+ (tan 30° + tan 15°)
= 2+ tan 30° tan 15°
+1 - tan 30° tan 15°
$\left(\because tan45^{\circ }=\frac{tan30^{\circ }+tan15^{\circ }}{1-tan30^{\circ }tan15^{\circ }}\right)$
$\Rightarrow 2+q-p=3$