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Math Help - Discriminants, roots and Polynomials (quick question)

  1. #1
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    Discriminants, roots and Polynomials (quick question)

    Hi, we've been studying polynomials at college recently and we've covered a lot of topics on it, but I'm stuck on one question. I remember doing questions like it, but we've gone over so much in the meantime that I've forgotten how to work it out!

    Find the set of values of k such that the equation x^2 + 4kx + 3k = 0 has two distinct roots.

    The discriminant (4k squared - 4(1)(3k)) has to be > 0 for it to have 2 distinct roots, but I forgot how to work it out!

    Any tips? Thanks =D
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  2. #2
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    So you need to solve the inequality
    (4k)^2-4(3k) >0

    16k^2-12k>0
    4k(4k-3) >0

    Can you solve this inequality (so the answer will be in terms of interval)
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  3. #3
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    Yeah, I can get to 4k(4k - 3) > 0 but I forgot what to do next =/

    I know that once I remember the method, I can work it out, but my mind's gone blank...
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  4. #4
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    Is it k > 3/4 ?

    Because don't you make each of the brackets equal 0 to find the intervals, so the brackets (4k)(4k - 3) would mean k would be > 0 and > 3/4

    I think I'm totally off, but I tried k as 0.74 and it didn't give a positive number, but 0.76 does, so it seems right...
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  5. #5
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     4k \ (4k - 3) > 0

    \Rightarrow 4k < 0 AND  4k - 3 > 0

    \Rightarrow k < 0 AND  k > \frac {3}{4}

    Apparently,  k cannot be both  < 0 AND  > \frac {3}{4}

    OR

     4k \ (4k - 3) > 0

     \Rightarrow 4k > 0 AND  4k - 3 < 0

     \Rightarrow k > 0 AND  k < \frac {3}{4}

    Combining these two inequalities, you get  0 < k < \frac {3}{4}.

    I hope that helps.

    me07.
    Last edited by ILoveMaths07; October 9th 2008 at 01:05 PM.
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