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Math Help - Quadratic Formula Help

  1. #1
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    Originally from Indianapolis, Indiana - but currently live in Haarlem, The Netherlands
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    Quadratic Formula Help

    I am working on a problem which requires the quadratic formula to solve. The problem is as follows:

    For which value(s) of p does the equation px^2 - 10x + p = 0 have exactly two solutions?

    I have plugged in the numbers and come up with:

    x = 10 +/- (√-10^2 - 4p^2)/2p

    From there I am unsure of what I need to do to get p by itself for the solution.

    Any help would be appreciated.

    Thanks,

    Matty
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  2. #2
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    Quote Originally Posted by AnAmericanInNederlands25 View Post
    I am working on a problem which requires the quadratic formula to solve. The problem is as follows:

    For which value(s) of p does the equation px^2 - 10x + p = 0 have exactly two solutions?

    I have plugged in the numbers and come up with:

    x = 10 +/- (√-10^2 - 4p^2)/2p

    From there I am unsure of what I need to do to get p by itself for the solution.

    Any help would be appreciated.

    Thanks,

    Matty
    You'd use the discriminant ( \Delta = b^2 - 4ac) but I don't understand the question.

    If \Delta > 0 then you have two, different real solutions
    If \Delta = 0 then you have two, identical real solutions
    If \Delta < 0 then you have two, different complex solutions

    The way your question is worded is ambiguous since all three cases give two solutions.

    If they meant equal solutions solve  b^2 - 4ac = 0

    (-10)^2 - 4 \cdot p \cdot p = 0

    100-4p^2 = 0

    (10-2p)(10+2p) = 0

    p = \pm 5
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