Final answer:
The zeros of the function f(x) = x⁴-2x³-7x²+5x-8 are x = 2 and x = -1. The zero x = 2 is in the interval (2, ∞) and the zero x = -1 is in the interval (-∞, -1).
Step-by-step explanation:
To find the zero(s) of the function f(x) = x⁴-2x³-7x²+5x-8, we need to set f(x) equal to 0 and solve for x. Using a graphing calculator or factoring, we find that the zeros of the function are x = 2 and x = -1. To determine the interval(s) in which the zeros are located, we can look at the sign of the function in different intervals.
- For x < -1, f(x) is positive
- For -1 < x < 2, f(x) is negative
- For x > 2, f(x) is positive
So the zero x = 2 is in the interval (2, ∞) and the zero x = -1 is in the interval (-∞, -1).