Question

A student claims that -4i is the only imaginary root of a quadratic polynomial equation that has real coefficients.

Answer 1

Step-by-step explanation:

Complex roots or imaginary roots must come in conjugate pairs.  If -4i is a root, that means 4i is also a root.

A possible polynomial is:

y = (x + 4i) (x − 4i)

y = x² − 16i²

y = x² + 16