Question

Using the conjugate zeros theorem to find all zeros of a polynomial

Answer 1

We know that 1+i is a root of the polynimial. This also implies that 1-i is also a root of the polynomial. In other words, the term

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

is a factor of our polynomial. This last expression can be written as

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

so, in order to find the remaining zero, we can compute the following division of polynomials,

which gives

Therefore, the remaining root is x=1.

In summary, the answer is:

`1+i,1-i,1`