## Precalculus (10th Edition)

$1$
The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa. The conjugate zeros are in pairs, therefore there must be an even number of them. The degree of the polynomial function is $5$ so it can have at most $5$ zeros. Since complex zeros come in conjugate pairs, then the polynomial function can have a maximum of four complex roots. Thus, the minimum number of real zeros of the polynomial function is $1$.