I don't even know where to start, teacher gave us this with no direction.

Question

Suppose the polynomial R(x)=a9x^9+a8x^8+...+a,x+a0 has real coefficients with a9 cannot equal 0. Suppose also that R(x)has the following zeros:

5,
6,
5+5i.
Using this information, answer the following questions.

(a) What is another zero of R(x)?
(b) At most how many real zeros of R(x) are there?
(c) At most how many imaginary zeros of R(x) are there?

Answer 1

a) 5-5i they come in pairs

b) 9 total, two are complex conjugates so 7

c) we have accounted for four, two real, two are complex conjugates. That leaves 5.
One of those must be real because complex roots come in paira
that leaves 4
or at most two pairs.