## College Algebra (10th Edition)

One of the missing zeros is $4+i$. The fourth zero must be a real number. The fourth zero cannot be a complex number since complex zeros come in pairs.
RECALL: The Conjugate Pairs Theorem states that if $a+bi$ is a zero of a polynomial function with real coefficients, then $a-bi$ is also a zero of the function. The function's degree is four so it has four zeros. Having $4-i$ as z zero of the given function means $4+i$ is also a zero of the function. Thus, three of the function's four zeros are $-3, 4-i, 4+i$. This means that the fourth zero cannot be a complex number since complex zeros come in pairs. Therefore, the fourth zero must be a real number.