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Rom4ik [11]
3 years ago
6

Given f(x) = x3 – 2x2 – x + 2, the roots of f(x)

Mathematics
2 answers:
anyanavicka [17]3 years ago
5 0

f(x) = x³ – 2x² – x + 2

 

 0 = x3 – 2x2 – x + 2

 (x-2)(x-1)(x+1)=0

 x1=-1

 x2=1

 x3=2

Leni [432]3 years ago
3 0

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

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