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

Charger421 Mar 4, 2021

#1**+1 **

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.

geno3141 Mar 4, 2021