Question

Determine where the real zeros of f(x) = x4 - 2x3 + x - 2 are located.

a. at -1 & 2
b. at 1 & 2
c. at 0 & 1
d. at -1 & 1

Answer 1

Explanation:

Step 1: Factor by grouping

`x^4 - 2x^3 + x - 2`

`x^3(x - 2) + 1(x - 2)`

`(x^3 + 1)(x - 2)`

Step 2: Solve for x

`x^3 + 1 = 0`

`x^3 = -1`

`\sqrt[3]{x^3} = \sqrt[3]{-1}`

`x = -1`

`x - 2 = 0`

`x - 2 + 2= 0 + 2`

`x = 2`

Answer:
`Option\ A, \ at\ -1 \ \& \ 2`