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.
The fourth degree polynomial function has the following zeros: $-3,2+i, 2-i, -3+5i$
By the Conjugate Pairs Theorem, $-3-5i$ must also be a zero of the given function. The function has degree $4$, so it can attain 4 zeros by the fundamental theorem of algebra.
Thus, $−3−5i$ cannot be another zero, so the given statement is false.
