Determine between which consecutive integers the real zeros

Option B: is the interval in which has a real zero

Explanation:

The given equation is

We need to determine x at which the value of f(x) becomes zero.

Option A:

Let us substitute the values of x in the equation f(x), we get,

(i) Consider the 1st interval

Since, there is a change of sign between the two interval, f(x) has a zero between the interval

(ii) Consider the 2nd interval

Since, there is no change of sign between the two interval, f(x) does not have a zero between the interval

(iii) Consider the 3rd interval

Since, there is no change of sign between the two interval, f(x) does not have a zero between the interval

(iv) Consider the 4th interval

Since, there is no change of sign between the two interval, f(x) does not have a zero between the interval

From all the above 4 options, there is no change of sign between the intervals and hence, Option A is not the correct answer.

Option B:

Let us substitute the values of x in the equation f(x), we get,

Since, there is a change of sign between the two interval, f(x) has a zero between the interval

Hence, Option B is the correct answer.

Option C:

Let us substitute the values of x in the equation f(x), we get,

Since, there is no change of sign between the two interval, f(x) does not have a zero between the interval

Hence, Option C is not the correct answer.

Option D:

Let us substitute the values of x in the equation f(x), we get,

Since, there is no change of sign between the two interval, f(x) does not have a zero between the interval

Hence, Option D is not the correct answer.