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8 October, 03:42

The function f is defined by f (x) x2 - 6x + 21. What are the solutions of f (x) 0?

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  1. 8 October, 04:09
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    f (x) = x^2 - 6x + 21

    0 = x^2-6x+21

    subtract 21 from each side to prepare for completing the square

    -21 = x^2 - 6x

    completing the square (b/2) ^2

    (-6/2) ^ = 3^2 = 9

    add 9 to each side

    -21 + 9 = x^2 - 6x + 9

    -21 + 9 = (x-3) ^2

    -12 = (x-3) ^2

    take the square root of each side

    + - sqrt (-12) = x-3

    add 3 to each side, take out the negative inside the square root

    3 + - i sqrt (12) = x

    simplify the square root sqrt (12) = sqrt (4) sqrt (3) = 2sqrt (3)

    3 + - i 2sqrt (3) = x

    Answer: 3+2isqrt (3)

    3-2isqrt (3)
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