Question

PLease help with step instructions, Im a mom trying to explain this to my child. Will award !

A student claims that -4i is the only imaginary root of a quadratic polynomial equation that has real coefficients.
a. what is the students mistake?
b. write one possible polynomial that has the correct roots from part a in standard form.

Answer 1

+4i is also a root.

Explanation:

Imaginary roots always occur in conjugate pairs.

This means that if -4i is a root of an equation then 4+i should also be a root. -4i can never be the only root.

So, the student's mistake is in claiming that -4i is the only root.

A quadratic equation which has +4i and -4i as roots: (x² + 4) = 0.