Degree 4, zeros:4 , multiplicity 2;6i

Question

Degrees 4 zeros 4 multiplicity 2;6i

Answer 1

I assume you seek a polynomial with real coefficients that has those zeros.  Note that if one of the zeros is complex, its complex conjugate must also be a zero (for the coefficients to be real).  So the zeros are

 

4

4

6i

-6i

 

The polynomial is

 

P(x) = A(x - 4)²(x - 6i)(x + 6i) = A(x - 4)²(x² + 36)

 

where A is any real number other than 0.  You can multiply it out to express P(x) in standard form if you wish.