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Math Help - [SOLVED] Quadratic formula??

  1. #1
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    Exclamation [SOLVED] Quadratic formula??

    please help!
    f(x) = X[squared] -Kx + 9 , where K is a constant.

    find the set values for K for which the equation f(x) = 0 has no real solutions.

    and

    given that k=4

    express f(x) in the form (x - p)2 + q, where p and q are constants to be found.

    thanks...
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  2. #2
    o_O
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    #1: Remember the discriminant?
    Given the quadratic ax^2 + bx + c = 0, if b^2 - 4ac \ {\color{red}<} \ 0 then there are no real solutions to x.

    So we must find when: k^2 - 4(1)(9) < 0

    Can you solve this?

    #2: y = x^2 -kx + 9 where k=4

    We must complete the square. So we take the coefficient of x, divide it by 2, square it, and add+subtract it (remember, it's an equation so we can't randomly change one side):
    \begin{array}{rcl} y & = & \big(x^2 - kx + {\color{red}\left(\frac{k}{2}\right)^2}\big) + 9 - {\color{red}\left(\frac{k}{2}\right)^2} \\ & \vdots & \end{array}

    Can you finish?
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  3. #3
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    Answer?

    so would it be:

    1: -6<k<6

    and

    2: (x + 2)2 + 5

    ?

    thanks
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