Question

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

Answer 1

Solution

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:

$x^4-8x^{3}+17x^2-8x+16$