If one root of the equation `x^(2)+px+q=0` is `2+sqrt(3)` where `p, q epsilon I` and roots of the equation `rx^(2)+x+q=0` are `tan 268^(@)` and `cot 88^(@)` then value of `p+q+r` is :

Options

A. `-1`
B. `-2`
C. `-3`
D. `-4`

Answer

B

Explanation

If one root of …………
`x^(2)+px+q=0` has one root `2+sqrt(3)` then other root
`= 2 - sqrt(3)`
"sum" of roots `= - (P)/(1)= 2+sqrt(3)+2-sqrt(3)`
`implies P = -4`
product of roots `= (q)/(1) = (2+sqrt(3))(2-sqrt(3))`
`implies q = 1` …..(i)
product of roots `= (q)/(1) = (2+sqrt(3))(2-sqrt(3))`
`implies q=1` ....(ii)
now `rx^(2)+x+q=0`
roots are tan `(268^(@)) tan (180^(@)+88^(@)) = tan 88^(@)` and `cot 88^(@)`
`:.` Product of roots `= tan 88^(@) .cot 88^(@) = (q)/(r )`
`implies 1 = (q)/(r ) implies q = r` ....(iii)
`:. p+q+r= -4+1+1= -2`