Write a polynomial function of least degree with rational coefficients so that P(x)=0 has the given root

Question

3-7i

P(x)= x^2 - __x +__

Answer 1

complex roots come in conjugate pairs, so if one is
3-7i, the other is 3+7i

sum of roots = 3-7i + 3+7i = 6
product of roots = (3-7i)(3+7i)
= 9 - 49i^2 = 9 + 49 = 58

equation is
x^2 - 6x +58 = 0