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22 August, 16:18

Find all zeros of the function g (x) = x^3-x^2-x+1

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  1. 22 August, 19:41
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    The zeroes of this equation would be - 1 and a double root at 1.

    Step-by-step explanation:

    To find these, start factoring by splitting. In this, we first only look at the first two terms. Then we pull out the greatest common factor.

    x^3 - x^2

    x^2 (x - 1)

    Now we do the same with the next two numbers.

    -x + 1

    -1 (x - 1)

    Now we can use the things outside the parenthesis along with the common parenthesis as the factors.

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

    And we can factor the first parenthesis by using the difference of two squares model.

    (x + 1) (x - 1) (x - 1)

    And finally, we can find the zeroes by setting each parenthesis equal to 0.

    x + 1 = 0

    x = - 1

    x - 1 = 0

    x = 1

    x - 1 = 0

    x = 1
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