Question

Determine between which consecutive integers the real zeros of f(x) = x^3 – 3x + 1 are located.

a. between -1&0, 0&1 and 2&3

C. between -1&0,0&1 and 1&2

b. between -2&-1, 0&1 and 1&2

d between -2&1, 0&1 and 1&2

Answer 1

B)
`-2 < x -1`,
`0 < x < 1` and
`1 < x < 2`

Explanation:

The value of the function evaluated at different points are described below:

`f(-2) = -1`

`f(-1) = 3`

`f(0) = 1`

`f(1) = -1`

`f(2) = 3`

The intervals where roots of the polynomial roots exists are:

`-2 < x -1`,
`0 < x < 1` and
`1 < x < 2`