Write a polynomial function of least degree with rational coefficients so that P(x)=0 has the given root 4-3i

Question

P(x)= x^2 - ?x + ?

(fill in the question marks)

Answer 1

The is is a quadratic with a pair of complex roots. The other root is 4+3i, the complex conjugate.

The equation is y = (x-4-3i)(x-4+3i).

Notice that when you multiply these binomials, it can be done as the sum and difference of 2 numbers.