## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The Conjugate Pairs Theorem states that when a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. This means that, when $(p +i \ q)$ is a zero of a polynomial function with a real number of the coefficients, then its conjugate $(p –i q)$, is also a zero of the function. We see that $2+i$ is zero of the polynomial function with real coefficients. This means that $2-i$ is also a zero of the function by the Conjugate Pairs Theorem. This implies that the polynomial function has at least $4$ zeros. However, the function does not have a degree of $4$, it has a degree of $3$. Thus we have a contradiction. Thus, the given statement is false.