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Math Help - Discriminants

  1. #1
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    Unhappy Discriminants

    What is the relationship between k, l and m in the quadratic equation: (k +1)x + 2/(k + m)x + (l + m) = 0 to have equal roots?

    Sorry but how exactly do I do this?
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    What is the relationship between k, l and m in the quadratic equation: (k +1)x + 2/(k + m)x + (l + m) = 0 to have equal roots?

    Sorry but how exactly do I do this?
    If the roots are equal then they must be repeated. If they're repeated then the discriminant is equal to zero.

    So get an expression for the discriminant and put it equal to zero. That will give the required relationship.
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  3. #3
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    Ummm I get 2* k^2 * l^2 + 2 * l^2 * m^2 + 8 * l^2 * k * m^2 - 2 * k^2 * m^2 - 2 * l^4 = 0. Is that the relationship??
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  4. #4
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    Quote Originally Posted by xwrathbringerx View Post
    Ummm I get 2* k^2 * l^2 + 2 * l^2 * m^2 + 8 * l^2 * k * m^2 - 2 * k^2 * m^2 - 2 * l^4 = 0. Is that the relationship??
    \Delta = \left( \frac{2}{k + m}\right)^2 - 4 (k^2 + l^2) (l^2 + m^2) = 0
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  5. #5
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    I managed to get that ... but I expanded it and got that massive equation ... wat exactly am I meant to do afterwards?
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  6. #6
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    Quote Originally Posted by xwrathbringerx View Post
    I managed to get that ... but I expanded it and got that massive equation ... wat exactly am I meant to do afterwards?
    Nothing. That's the relationship between k, l and m, as asked for.
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