Determine between which consecutive integers the real zeros of f (x) = x^4-8x^2+10 are located.

a. between (-3 & - 2) and (-2 & - 1)

c. both a & b

b. between (1 & 2) and (2 & 3)

d. no real zeros

f (x) has a zero for x between - 3 and - 2, for x between - 2 and - 1, for x between 1 and 2 and for x between 2 and 3

Explanation:

We need to create a table with the values for the function f (x) = x⁴ - 8x² + 10 within the integer interval - 3 ≤ x ≤ 3

x: - 3 - 2 - 1 0 1 2 3

f (x) : 19 - 6 3 10 3 - 6 19

f (-3) is positive and f (-2) is negative, from the location principle, f (x) has a zero between - 3 and - 2

f (-2) is negative and f (-1) is positive, from the location principle, f (x) has a zero between - 2 and - 1

f (1) is positive and f (2) is negative, from the location principle, f (x) has a zero between 1 and 2

f (2) is negative and f (3) is positive, from the location principle, f (x) has a zero between 2 and 3

f (x) has a zero for x between - 3 and - 2, for x between - 2 and - 1, for x between 1 and 2 and for x between 2 and 3