Answer
False
Work Step by Step
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 $i$ and $3+i$ are zeros of the polynomial function with real coefficients. This means that $-i$ and $3-i$ are also zeros of the function by the Conjugate Pairs Theorem. But the polynomial function has a degree of $3$, so the function can have only $3$ zeros, which is a contradiction.
Thus, the given statement is false.
