Final answer:
The polynomial with real coefficients that has 2 and 2-i as zeroes is x^3 - 6x^2 + 13x - 10.
Step-by-step explanation:
The polynomial with real coefficients that has 2 and 2-i as zeroes can be found by using the fact that complex zeroes come in conjugate pairs. Given that 2-i is a zero, its conjugate 2+i must also be a zero. We can then find the polynomial by multiplying the factors (x-2)(x-(2+i))(x-(2-i)).
Expanding this expression, we get (x-2)(x-2-i)(x-2+i) = (x-2)(x^2-4x+5).
Therefore, the polynomial with real coefficients is x^3 - 6x^2 + 13x - 10