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Math Help - discriminant

  1. #1
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    discriminant

    Please show this step by step and it'll be even better if there are some explanations for the solution!

    Find the values of p for which the equation (1 - 2p)x^2 +8px - (2 + 8p) = 0 has one solution.


    And hey, can you guys make up a question for me as well that's similar to this one?
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  2. #2
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    read the section called Discriminant in the following article:

    Quadratic equation - Wikipedia, the free encyclopedia
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  3. #3
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    Quote Originally Posted by delicate_tears View Post
    Please show this step by step and it'll be even better if there are some explanations for the solution!

    Find the values of p for which the equation (1 - 2p)x^2 +8px - (2 + 8p) = 0 has one solution.


    And hey, can you guys make up a question for me as well that's similar to this one? Mr F says: Surely your textbook has plenty of them ....?
    \Delta = (8p)^2 - 4(1 - 2p)(-(2 + 8p)) = 64 p^2 + 8(1 - 2p)(1 + 4p) = 16p + 8.
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  4. #4
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    Quote Originally Posted by delicate_tears View Post
    Please show this step by step and it'll be even better if there are some explanations for the solution!

    Find the values of p for which the equation (1 - 2p)x^2 +8px - (2 + 8p) = 0 has one solution.


    And hey, can you guys make up a question for me as well that's similar to this one?
    The quadratic equation gives:

    x=\frac{-8p \pm \sqrt{64p^2 + 4(2 + 8p)(1 - 2p)}}{2-4p}

    We want that discriminant to be equal to zero.

    \sqrt{64p^2 + 4(2 + 8p)(1 - 2p)} = 0
    64p^2 + 4(2 + 8p)(1 - 2p) = 0
    64p^2 + 4(2 - 4p + 8p - 16p^2) = 0
    64p^2 + 8 +16p - 64p^2 = 0
    8 +16p= 0
    16p= -8
    p= \frac{-1}{2}

    Plug p back into the original equation, and you will get your one solution for x.
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