A polynomial function is described Find all remaining zeros

A polynomial function is described. Find all remaining zeros.

a. Degree: 3 Zeros: -1, i

b. Degree: 6 Zeros: -2 (multiplicity 2), 1-5i, 2+3i

c. Degree: 6 Zeros: 2i, 1+i (multiplicity 2)

Solution

a) Complex roots are always exist in conjugate pair.
conjugate pair of a+ib is a-ib
So third root will be conjugate pair of i, which is -i.
So all three roots are -1,i and -i .
b)Conjugate pair of 1-5i is 1+5i and conjugate pair of 2+3i is 2-3i . So all roots are -2 (multiplicity 2), 1-5i, 2+3i, 1+5i and 2-3i.
c) Conjugate pair of 2i is -2i and conjugate pair of 1+i with 1-i with multiplicity -2 . 2i, 1+i (multiplicity 2), 1 - i(multiplicity 2) and -2i.