Question

Which of the following is a polynomial with roots 3, -3i, and 3i ?

Answer 1

do you even know what a "root" stand for on a polynomial?

Answer 2

And choices are?

Answer 3

Well, a polynomial \(P(x)\) with roots at \(x = 3, x = \pm 3i\) can be written in the form

\[P(x) = k(x-3)(x-3i)(x+3i)\] where \(k\) is a non-zero constant. At a root, the polynomial will equal 0, and this form will give a value of 0 at any of the specified roots, and nowhere else. The constant \(k\) just amplifies or shrinks the curve in the y direction, but does not change the location of the roots. It's possible that your answer choices involve expanding the polynomial, but without seeing them, it's hard for us to know.