Question

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

Answer 1

C. both a and b.

Step-by-step explanation:

The dude above explained it perfectly, but did not directly state the answer.

Answer 2

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

Step-by-step 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