Question

How do you write a polynomial with zeros: 2i, sqrt2, and 2?

Answer 1

`x^3-(2+sqrt2+2i)x^2+(2sqrt2+(2sqrt2+4)i)x-4sqrt2i`

Explanation:

The polynomial with zeros: `2i,sqrt2` and `2` is

`(x-sqrt2)(x-2)(x-2i)` or

`(x^2-sqrt2x-2x+2sqrt2)(x-2i)` or

`(x^3-sqrt2x^2-2x^2+2sqrt2x-2ix^2+2sqrt2ix+4ix-4sqrt2i)` or

`x^3-(2+sqrt2+2i)x^2+(2sqrt2+(2sqrt2+4)i)x-4sqrt2i`