Final answer:
The real zeros of the polynomial 2.5x^4 + 3x^3 - 2.6x^2 - 5.1x - 5.6 are approximately x = -2.2, -1, 0.4, and 1.6.
Step-by-step explanation:
To find the real zeros of the polynomial, we need to solve the equation 2.5x^4 + 3x^3 - 2.6x^2 - 5.1x - 5.6 = 0.
One way to solve this equation is to use the Rational Root Theorem to find potential rational roots. By examining the factors of the constant term -5.6 (or 5.6), we can find the possible rational roots.
Using synthetic division, we can test these possible roots and determine which ones result in a remainder of zero, indicating a real zero. By doing this, we find that the real zeros of the polynomial are approximately x = -2.2, -1, 0.4, and 1.6.