Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.

Question

   3-i,sqrt2

f(x)=??

Answer 1

since the coefficients are rational, the roots come in conjugate pairs. So, the roots are

3-i, 3+i, √2, -√2

f(x) = (x-(3-i))(x-(3+i))(x-√2)(x+√2)
= (x^2-6x+9+1)(x^2-2)
= ...