Question

How do you write the polynomial function with the least degree and zeroes i, 4?

Answer 1

The requested polynomial is

`(x-i)(x-4)=x^2-x(4+i)+4i=0`

Answer 2

If the polynomial is also to have Real coefficients, then it must also have `-i` as a zero, so:

`f(x) = (x-i)(x+i)(x-4) = (x^2+1)(x-4)`

`= x^3-4x^2+x-4`

Explanation:

Complex roots of polynomial equations with Real coefficients always occur in conjugate pairs.

Note that any polynomial that has these roots will be a multiple (scalar or polynomial) of `f`.