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If 2+sqrt(3)i is a root of the equation ...

If `2+sqrt(3)i` is a root of the equation `x^2+p x+1=0` , then write the values of `p\ a n d\ q` .

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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`
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