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27 November, 23:30

If f (x) = x^2 - 4 (x) + 6, find x if f (x) = 27

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  1. 28 November, 01:09
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    x = - 3 or x = 7

    Step-by-step explanation:

    Given

    f (x) = x² - 4x + 6

    If f (x) = 27, then equating gives

    x² - 4x + 6 = 27 (subtract 27 from both sides)

    x² - 4x - 21 = 0 ← in standard form

    Consider the factors of the constant term ( - 21) which sum to give the coefficient of the x - term ( - 4)

    The factors are - 7 and + 3, since

    - 7 * 3 = - 21 and - 7 + 3 = - 4, hence

    (x - 7) (x + 3) = 0

    Equate each factor to zero and solve for x

    x + 3 = 0 ⇒ x = - 3

    x - 7 = 0 ⇒ x = 7
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