Question

write a polynomial function of the lowest degree with rational coefficients that has the given numbers as some of its zeros: 2-i, sqrt(3)

Answer 1

We need to counterbalance the zero 2-i with 2+i and the zero √3 with -√3. That gives us 4 zeroes and a 4th degree polynomial: (x-2-i)(x-2+i)(x-√3)(x+√3)=(x^2-2x+5)(x^2-3)=x^4-2x^3+2x^2+6x-15.