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:

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