Question

If roots of equation x² + px + q = 0 are tan30° and tan15° then value of 2 + q – p is

(a) 1

(b) 2

(c) 3 

(d) 0

Answer 1

The correct option (c) 3

Explanation:

tan30° + tan15° = sum of roots = – p

tan30° ∙ tan15° = product of roots = q

Now 1 = tan45 = [(tan30° + tan15°) / (1 – tan30° ∙ tan15°)]

∴ 1 = [(– p) / (1 – q)] 

∴ 1 – q + p = 0

∴ 2 + q – p = 2 + 1 = 3.