Answer:
A, B, D, F
Step-by-step explanation:
You want to know the intervals containing a zero of the given function ...
f(x) = x⁴ -3x³ -2x² +5x +1
Zeros
An interval will contain a zero of the function if the function value changes sign from one end of the interval to the other. This means we can evaluate the function for integers -2 to +4 and identify the sign changes to determine the intervals.
The function Y0(x) in the attachment is defined the same as f(x) in the problem statement. It shows us there are sign changes in the following intervals:
- [-2, -1] . . . . A
- [-1, 0] . . . . . B
- [1, 2] . . . . . . D
- [3, 4] . . . . . . F
