Question

How do you write a polynomial with zeros 2,-2,-6i?

Answer 1

Polynomial is `x^3+6ix^2-4x-24i`

Explanation:

A polynomial with zeros as `a, b, c` is `(x-a)(x-b)(x-c)`, as each of `a, b, c` make the vale of polynomial zero

Hence, A polynomial with zeros as `2, -2, -6i` is

`(x-2)(x-(-2))(x-(-6i))` i.e.

`(x-2)(x+2)(x+6i)` or

`(x^2-4)(x+6i)` or

`x^3+6ix^2-4x-24i`