Find a polynomial equation with real coefficients that has the given roots 1 and -6i

Answer 1

The complex conjugate of a complex root must also be a root, so you will have three roots:

1

6i

-6i

f(x) = A(x - 1)(x - 6i)(x + 6i)

A is real and A≠0.

f(x) = A(x - 1)(x² + 36)

You can expand this further if you wish.