Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 3-i, square root of 7

Real coefients

if a+bi is a root then a-bi is also a root

since 3-i is a root then 3+i s also a root

also the √7, so if √7 is a root then - √7 is also a root

so

f roots are r1 and r2 then the factored form is

f (x) = (x-r1) (x-r2)

roots are 3-i, 3+i and √7 and - √7

f (x) = (x - (3-i)) (x - (3+i)) (x-√7) (x - (-√7))

expanded

f (x) = x⁴-6x³+3x²+42x-70