How do you write a 4th degree polynomial with zeros 1, 2, and i?

Question

How do you write a 4th degree polynomial with zeros 1, 2, and i?

Answer 1

since we have 3 zeros that means we have 2 same zeros as a solution to 4th degree equation.The way we write out the equation would be the following

(x-1)(x-2)(x-i)²=0

Answer 2

The expressions would be: f(x) = (x-1)(x-2)(x-i)(x+i)

Anytime you have zeros (roots) at for example sqrt(6) or (2-3i) your

expresses would be (x+sqrt(6))(x-sqrt(6)) or (2-3i)(2+3i)

Look into the difference of two squares: (a^2 - b^2) = (a+b)(a-b)

Hope this helps.

Richard