Question

I have two questions that I don't understand and need help with.

1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f.

degree 4, zeros i;9+i

2. form a polynomial f(x) with real coefficients having the given degree and zeros.

degree 4, zeros 3, multiplicity 2; 6i

f(x)=a(?)

Answer 1

1.
Need four zeros but every complex root comes with its complex conjugate
i so also -i
9+i so also 9-i

(x-3)(x-3)(x- 6i)(x+6i)
multiply that out