Question

How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 2i, -2i?

Answer 1

`f(x) = x^2+4`

Explanation:

Let `f(x)` be the polynomial of degree 2 and leading coefficient 1 with zeros `+-2i`

Hence either `(x+2i)` or `(x-2i) = 0`

`:. f(x) = 0 = (x+2i)(x-2i)`

`f(x) = x^2 +2ix -2ix -4i^2`

`f(x) = x^2 +4`