Find a function P(x) of least possible degree, having real coefficients, with the given zeros. 2 and 6i

Answer 1

In order to have real coefficients, the complex conjugate of a complex zero must also be a zero, so you have three zeros:

2

6i

-6i

Then P(x) is of degree 3:

P(x) = A(x - 2)(x - 6i)(x + 6i) = A(x - 2)(x² + 6)

where A is any real number ≠ 0.