Final answer:
The maximum number of non-real zeros possible for the fourth-degree polynomial function f(x) is four, which would occur if all zeros were complex and hence come in two pairs of complex conjugates.
Step-by-step explanation:
The maximum number of non-real zeros possible for the function f(x) = 2.5x4 + 3x3 - 2.6x2 - 5.1x - 5.6 is determined by the Fundamental Theorem of Algebra.
This theorem states that any non-constant single-variable polynomial with real or complex coefficients has as many complex zeros as its degree when counted with multiplicity.
Hence, a fourth-degree polynomial will have four zeros in total.
Real zeros are x-values where the graph of the function crosses the x-axis. Complex zeros come in conjugate pairs, which mean for every non-real zero, there is another that is its complex conjugate.
Thus, the maximum number of non-real zeros for this fourth-degree polynomial would occur if all of them were non-real, and since they come in pairs, we would have two pairs of complex conjugate zeros, meaning four non-real zeros.