Question

How do you write a polynomial function of least degree that has real coefficients, the following given zeros 2, -1+i, -1-i?

Answer 1

`f(x)=x^3-2x-4`

Explanation:

Each zero corresponds to a linear factor.

So we can write:

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

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

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

`=(x-2)(x^2+2x+2)`

`=x^3-2x-4`

Any polynomial in `x` with these zeros will be a multiple (scalar or polynomial) of this `f(x)`.