Question

How do you write a polynomial with zeros 2i, 3i, 1?

Answer 1

`x^5-x^4+13x^3-13x^2+36x-36=0`

Explanation:

Complex roots occur in conjugate pairs. So, the roots are `1, +-2i, +-3i,`. The degree of the polynomial is 5.

Hence, the polynomial equation is

`(x-1)((x-2i)(x+2i))((x-3i)(x+3i))=0`

`(x-1)(x^2+2^2)(x^2+3^2)=0`

Expanding,

`x^5-x^4+13x^3-13x^2+36x-36=0`