Question

4) Degree 6, zeros 4,5, 4-5i,-5+i A) 4, 4+5i,-5-i B) 4, 4+5iC)4+5i,-5-i D)-4+5i, 5 -i

Answer 1

$\begin{gathered} \text{ If a complex number a+bi is a zero of a polynomial, then its conjugate (a-bi)} \\ \text{ is also a zero of the polynomial. so, since 4-5i is a zero, } \\ 4+5i\text{ must be a zero of the polynomial.} \\ \text{ In the same way, since -5+i is a zero of the polynomial, } \\ -5-i\text{ must be a zero of the polynomial too.} \end{gathered}$

And the answer is C).