Final answer:
a) The value of gF(24) depends on the function gF, not provided.
b) Roots of the irreducible polynomial x2+1 are x=i and x=−i.
c) The derivative of x2+1 is 2x.
d) The integral of gF(24) with respect to x cannot be determined without the specific form of gF.
Step-by-step explanation:
It seems like there might be some confusion or missing information in your question. The notation "gF(24)" is not standard in mathematical expressions. However, I can provide some general guidance based on what you've given:
a) To find the value of gF(24), you need to know the function gF and substitute 24 into it.
b) The irreducible polynomial x2+1 has complex roots since it is of the form a2+b2, which corresponds to the sum of two squares. The roots are
x=i and x=−i, where i is the imaginary unit.
c) The derivative of the irreducible polynomial x2+1 with respect to x is
2x.
d) Without knowing the specific form of the function gF, it's not possible to find the integral. You would need the function to determine the integral of gF(24) with respect to x.
If you provide more details about the function gF, I can offer a more specific answer.