Question

Write a polynomial function of least degree with rational coefficients so that P(x)=0 has the given root 3-i

Answer 1

Since all complex roots come in conjugate pairs, there has to be

another root of 3+i, so the least number of roots is 2

sum of roots = 3-i + 3+i = 6
product of roots = (3-i)(3+i) = 9 - i^2 = 10

P(x) = x^2 - 6x + 10

another way:
P(x) = (x - (3-i) )(x - (3+i) )
= .....