Final answer:
To find the zeros of the given fourth-degree polynomial, potential rational zeros should be considered and tested. If a zero is found, the polynomial is divided by its factor to reduce its degree and proceed until a quadratic equation is formed, which can be solved using the quadratic formula. The provided options are incomplete as the polynomial could have up to four zeros.
Step-by-step explanation:
To find the zeros of the polynomial function f(x) = x⁴ - 4x³ - 22x² + 4x + 21, we can attempt to use the Rational Root Theorem to find potential rational zeros, and then apply polynomial division or synthetic division to test these candidates. Once we find one zero, we can divide the polynomial by the corresponding factor to reduce its degree and eventually arrive at a quadratic equation, which can be solved using the quadratic formula.
Unfortunately, the options provided do not include all the zeros, as this is a fourth-degree polynomial and therefore has up to four real or complex zeros. To determine the correct options provided, we would need to either use the synthetic or long division method to factorize the polynomial or apply numerical methods if the roots cannot be easily factored. The options present only pairs of roots, so without further work, we cannot say with certainty which option is correct.