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Math Help - Need help with what is probably a simple quadratic equation

  1. #1
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    Need help with what is probably a simple quadratic equation

    Hi, I really need a hand with the following question

    Find the values for k for which the quadratic equation x^2-2x+21=2k(x-7) has equal roots

    I don't really know what to do, I know the discriminant must equal 0 but actually putting that usefully is completely beyond me somehow.

    Any help you could provide would be much appreciated.
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  2. #2
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    Solve for x in terms of k.

    Get the equation in the form ax^2 + bx + c = 0. k will be in there somewhere in a,b, and/or c. Then, solve the quadratic. Instead of simplifying the qudratic formula to a constant, simplify it to terms with k.

    Does that make sense? Shout at me if it doesn't.
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  3. #3
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    Quote Originally Posted by finlaymaguire View Post
    Hi, I really need a hand with the following question

    Find the values for k for which the quadratic equation x^2-2x+21=2k(x-7) has equal roots

    I don't really know what to do, I know the discriminant must equal 0 but actually putting that usefully is completely beyond me somehow.

    Any help you could provide would be much appreciated.
    rearrange the equation as:

    <br />
x^2-2(1+k)x+28=0<br />

    Now the quadratic formula tells us that:

    <br />
x=\frac{2(1+k) \pm \sqrt{4(1+k)^2-4\times 28}}{2}<br />

    There are two distinct roots unless what is under the root (the
    discriminant is zero), when there is only one root (or two equal roots).
    So the condition for a double root is that:

    <br />
4(1+k)^2-4\times 28=0<br />

    RonL
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  4. #4
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    ahhhh, I can't believe I couldn't see that, so would that make the values of k be 2 and -10/9?

    Thanks for the help by the way, I really appreciate it.
    Last edited by finlaymaguire; November 21st 2006 at 01:00 PM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by finlaymaguire View Post
    ahhhh, I can't believe I couldn't see that, so would that make the values of k2 and -10/9?

    Thanks for the help by the way, I really appreciate it.
    No it would be:

    <br />
k=-1 \pm \sqrt{28}<br />

    RonL
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