Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros -3; -i; -9+i.
Most important thing to remember here is that complex zeros come in conjugate pairs. This means that if −i is zero of polynomial, then its conjugate pair, i must also be a zero.
Thus, zeros of polynomial are: −3,−i,i,−9+i,−9−i
Now, we can write polynomial in factored form:
Also, notice that since polynomial has five roots, its degree is five.