Find the constant term of a quartic polynomial with rational coefficients that has two roots equal to 2 − i and 2 +√3

Since one root is  2 - i  another root will be  2 + i.

 

Since one root is  2 + sqrt(3)  another root will be  2 - sqrt(3).

 

Written as factors:  [ x - (2 - i) ] · [ x - (2 + i) ] · [ x - (2 + sqrt(3)) ] · [ x - (2 - sqrt(3)) ]  =  0

 

Multiply this out and select the constant term.

 

However, since this answer can be multiplied by any non-zero constant and still have the same roots, any non-zero constant will work.