If the sum of square of roots of equation `x^2+(p+iq)x+3i=0` is 8, then find |p|+|q| , where p and q are real.

Options

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

Answer

C

Explanation

Let the roots be `alpha` and `beta`
We have `alpha + beta = -(p + iq),alpha beta = 3i`
Given: `alpha^(2) + beta^(2) = 8`
`or (alpha+beta)^(2) - 2alpha beta = 8`
`or (p + iq)^(2) -6i(2pq-6) = 8`
`or p^(2)-q^(2) + (2pq -6) = 8`
`or p^(2) -q^(2) =8 and pq =3`
`rArr p = 3 and q=1 or p=-3 and q=-1`