Answer
$-3$ and $5i$
Work Step by Step
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.
Its degree is $3$, hence it has $3$ complex zeros. According to the Conjugate Pair Theorem since $-5i$ is a complex zero, $5i$ is also a complex zero.
Assume $r$ is the last zero.
Then we know that
\begin{align*}
(x-5i)(x-(-5i))(x-r)&=x^3+3x^2+25x+75\\(x-5i)(x+5i)(x-r)&=x^3+3x^2+25x+75\\(x^2+25)(x-r)&=x^3+3x^2+25x+75\\x^3-rx^2+25x-25r&=x^3+3x^2+25x+75\end{align*}
Thus,
$-25r=75\\
r=-3$
