Final answer:
To determine consecutive values of x between which each real zero is located in the function f(x)=x⁴-2x³-5, we can factor the function and find the zeros.
Step-by-step explanation:
To determine the consecutive values of x between which each real zero is located in the function f(x) = x⁴-2x³-5, we need to analyze the behavior of the function and find the intervals where it is positive or negative.
By factoring the function, we have f(x) = (x-1)(x+1)(x²-2x-5). Setting each factor equal to zero, we find the real zeros x = -1, x = 1, and the zeros of the quadratic equation, which are approximately x ≈ -1.236 and x ≈ 3.236.
Therefore, the consecutive values of x between which each real zero is located are -3 ≤ x ≤ -1, -1 ≤ x ≤ 1, and 1 ≤ x ≤ 3.