Find a polynomial function of lowest degree with rational coefficients that has 3-i, and √7 as some of its zeros

Question

Thank you!

Answer 1

Then 3+i and -sqrt(7)= -rad7  will also be zeros

 

 

(x - 3 + i)(x - 3 - i)(x + rad7)(x - rad7)

 

[(x-3)^2 - i^2 ][x^2 - rad7^2]

 

[(x-3)^2 + 1][x^2 - 7]

 

(x^2 - 6x + 10)(x^2 - 7)

 

x^4 - 6x^3 + 10x^2

                      - 7x^2 + 42x - 70

 

=

x^4 - 6x^3 + 3x^2 + 42x - 70