Question

Find a polynomial of given degree with given zeros: complex zeros

Answer 1

For this case we have the following roots:

4 (multiplicity 2) and i

Therefore we can create the following expression

`(x-4)(x-4)(x-i)(x+i)`

Solving we have:

`(x^2-8x+16)(x-i)(x+1)=(x^(2)-8x+16)(x^(2)+1)`
`x^(4)+x^(2)-8x^(3)-8x+16x^(2)+16`

Simplifying we got:

`x^4-8x^(3)+17x^2-8x+16`