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5 August, 07:29

Determine which consecutive integers do not have a real zero of f (x) = x^3+5x^2 - x - 6 between them.

(-6,-5)

(-2,-1)

(-5,-4)

(1,2)

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  1. 5 August, 08:08
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    (-6, - 5).

    Step-by-step explanation:

    If there is a zero between the integers there will be a change of sign of f (x).

    x^3 + 5x^2 - x - 6

    f (1) = 1 + 5 - 1 - 6 = - 1

    f (-1) = - 1 + 5 + 1 - 6 = - 1

    f (2) = 8 + 20 - 2 - 6 = 20

    There' a change of sign between f (1) and f (2) so there is a zero between (1, 2).

    f (-2) = - 8 + 20 + 2 - 6 = 6

    So there is also a zero between - 1 and - 2. (-2, - 1)

    F (-4) = 14, f (-5) = - 1 = change of sign so there is also a zero in (-5,-4)

    f (-6) = - 36 - no change in sign between - 5 and - 6.
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