write a polynomial function f(x) with zeros 1, -2/3, and 3i

Answer 1

write a polynomial function f(x) with zeros 1, -2/3, and 3i.

Every time that you have a complex root, it should always be accompanied by its complex conjugate. Therefore, you have 4 roots namely, 1, -2/3, 3i, and -3i, and the polynomial will accordingly be:

f(x) = (x - 1)(x + 2/3)(x^2 +9). Distribute so you can get your 4th-order polynomial.