State how many imaginary and real zeros the function has.

f (x) = x3 + 5x2 - 28x - 32

We are asked to solve and determine how many imaginary and real zeroes in the given expression shown below:

f (x) = x3 + 5x2 - 28x - 32

We need to perform factorization of (x+1) from the given function such that the problem become:

x3 + 5x2 - 28x - 32

(x+1) (x2 + 4x - 32), now we need to perform factorization of (x2 + 4x - 32)

this can be a combination of numbers + 8 and - 4 such that

(x+1) (x+8) (x-4)

From the solution, we clearly see that there were three real zeroes in the given function.

The answer is "0 imaginary, 3 real".