Question

Given f(x) = x3 – 2x2 – x + 2,

the roots of f(x)

Answer 1

f(x) = x³ – 2x² – x + 2

0 = x3 – 2x2 – x + 2

(x-2)(x-1)(x+1)=0

x1=-1

x2=1

x3=2

Answer 2

For this case we must follow the steps below:

We factor the polynomial, starting by factoring the maximum common denominator of each group:

`x ^ 2 (x-2) - (x-2)`

We factor the maximum common denominator
`(x-2):`

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

Now, by definition of perfect squares we have:

`a ^ 2-b ^ 2 = (a + b) (a-b)`

Where:

`a = x\\b = 1`

Now, we can rewrite the polynomial as:

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

To find the roots we equate to 0:

`(x-2) (x + 1) (x-1) = 0`

So, the roots are:

`x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1`

Answer:

`x_ {1} = 2\\x_ {2} = - 1\\x_ {3} = 1`