Degree​ 4; ​ zeros: 5 - 5 i ; - 4 multiplicity 2

Question

enter  the polynomial

Answer 1

Assuming you want the coefficients to be real (which you did not state in the problem description), the complex conjugate of a complex zero must also be a zero.  Therefore, the 4 zeros are

 

5 - 5i

5 + 5i

-4

-4

 

f(x) = A[x - (5 - 5i)][x - (5 + 5i)](x + 4)²,

 

where A is any real number ≠ 0.  You can expand this into standard form if you wish.