Polynomial function

Question

What is the polynomial function of the lowest degree with lead coefficient 1, and roots 1+ I?

Answer 1

It's not so clear what is being asked. Are the roots 1 and 1, which is really one root, but perhaps in this form since it's from a quadratic? or 1 and i (imaginary)? or maybe even 1 +/- i ?

If just one root 1, f(x) = x - 1

If 2 roots 1, f(x) = (x - 1)² or x² - 2x + 1

If 1 +/- i, then f(x) = x² - 2x + 2

Remember, (x - root) = 0.

If these guesses about the desired roots are not right, please send a revision of the problem in he comments.

Answer 2

f(x) = (x + 2)²