if ` 2+isqrt3` be a root of the equation ` x^(2) + px + q =0`, where p and q are real, then find p and q

Explanation

Accordingly ` 2 + isqrt3` is a root of the equation ` x^(2) + px + q =0` ,then other root must be ` 2 -isqrt3` now sum of roots =` -p = ( 2 + sqrt3) + ( 2- isqrt3)= 4`
` Rightarrow p =-4`
Product of roots ` = q = ( 2 + isqrt3) (2 -isqrt3) , ( 2+ isqrt3) ( 2 -isqrt3) = 4 -3i^(2)=7`