Question

If the roots of the quadratic eqn x²+px+q=0 are tan 30° and tan 15° respectively, then the value of 2+q-p is-

Answer 1

the quadratic must have been

(x-tan30)(x-tan15) = 0
x^2 - xtan30 - xtan15 + tan30tan15 = 0
x^2 + x(-tan30 - tan15) + tan30tan15 = 0

comparing this to x^2 + px + q = 0
p = -tan30 - tan15 and q = tan30tan15

then 2 + q - p = 2 + tan30tan15 - (-tan30 - tan15)
= 2 + tan30tan15 + tan30 + tan15