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Math Help - repeated roots

  1. #1
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    repeated roots

    here's the question: the following equation has repeated roots. find the value of the constant p leaving your answer in exact form:

    px^2 - 5x + p = 0

    could someone show me the method to figure that out please?

    thanks

    ps the answer is p = \pm \frac{5}{2}
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  2. #2
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    Quadratic with repeated roots

    Hello mark
    Quote Originally Posted by mark View Post
    here's the question: the following equation has repeated roots. find the value of the constant p leaving your answer in exact form:

    px^2 - 5x + p = 0

    could someone show me the method to figure that out please?

    thanks

    ps the answer is p = \pm \frac{5}{2}
    It's worth learning that the quadratic equation ax^2+bx+c=0 has repeated roots if and only if the discriminant is zero. That means b^2 - 4ac = 0

    So here: a = p, b = -5 and c = p. And when we plug these in to b^2-4ac = 0, we get:

    25-4\times p \times p = 0

    \Rightarrow 4p^2 = 25

    \Rightarrow p^2 = \frac{25}{4}

    \Rightarrow p = \pm\frac52

    Grandad
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  3. #3
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    You know that px^2 - 5x + p = 0 has one repeated root.

    What does this tell you about the discriminant?

    Nevermind, grandad ahead of me ;x
    Last edited by Defunkt; September 7th 2009 at 06:40 AM.
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