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16 May, 05:35

Which is a zero of the quadratic function f (x) = 9x2 - 54x - 19?

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Answers (2)
  1. 16 May, 05:42
    0
    F (x) = 9x² - 54x - 19 = 9x² - 57x + 3x - 19 = 3x (3x - 19) + 1 (3x - 19)

    = (3x - 19) (3x + 1)

    f (x) = 0 if 3x - 19 = 0 or 3x + 1 = 0

    3x = 19 or 3x = - 1

    x = 19/3 or x = - 1/3

    (all credit goes to dalendrk)
  2. 16 May, 05:55
    0
    Let's complete the square

    isolate x terms

    f (x) = (9x²-54x) - 19

    undistribute quadratic coefient

    f (x) = 9 (x²-6x) - 19

    take 1/2 of linear coefient (-6) and square it

    -6/2=-3, (-3) ²=9

    add positive and negative of it inside parenthasees

    0=9 (x²-6x+9-9) - 19

    copmlete the square

    0=9 ((x-3) ²-9) - 19

    distribute

    0=9 (x-3) ²-81-19

    0=9 (x-3) ²-100

    add 100 to both sides

    100=9 (x-3) ²

    divide both sides by 9

    100/9 = (x-3) ²

    sqrt both sides, remember positive and negative roots

    +/-10/3=x-3

    rewrite 3 as 9/3

    add 9/3 to both sides

    9/3+/-10/3=x

    so

    9/3+10/3=x or 9/3-10/3=x

    19/3=x or - 1/3=x

    the zeroes are at x=19/3 and - 1/3
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