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9 September, 02:50

Factor. Find the roots. Show your work.

f (n) = n^2 - 6n - 16

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  1. 9 September, 04:05
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    n = - 2, n = 8

    Step-by-step explanation:

    To obtain the roots equate f (n) to zero, that is

    n² - 6n - 16 = 0

    To factor consider the quadratic

    Consider the factors of the constant term ( - 16) which sum to give the coefficient 0f the n - term ( - 6)

    The factors are - 8 and + 2, since

    - 8 * 2 = - 16 and - 8 + 2 = - 6, hence

    (n - 8) (n + 2) = 0

    Equate each factor to zero and solve for n

    n - 8 = 0 ⇒ n = 8

    n + 2 = 0 ⇒ n = - 2
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