Answer
2 real zeros,
4 imaginary (complex, nonreal) zeros
Work Step by Step
see Properties of Roots of Polynomial Equations (page 382)
1. If a polynomial equation is of degree $n$, then counting multiple roots separately, the equation has $n$ roots.
2. If $a+bi$ is a root of a polynomial equation with real coefficients $(b\neq 0)$, then the imaginary number $a-bi$ is also a root.
Imaginary roots, if they exist, occur in conjugate pairs.
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The graph (attached image) crosses the x-axis at two places,...
f has 2 real zeros.
It has a total of n=6 zeros, so there are another
two pairs of conjugate complex zeros, 4 in all