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Math Help - Equation

  1. #1
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    Equation

    Given α and β are the roots of the quadratic equation px^2+qx+r=0, find the relationship between p,q and r if

    a)
    α=2β+1
    b)
    α=3β+1

    Answers provided by the answer sheet are 2q^2 + pq - p^2 = 9pr and 3q^2 + 2pq - p^2 =16pr respectively.


    As shown below, i just managed to solve a) but not b), in both solutions for b, i don't know what goes wrong and they are not same as the answer provided, it is possible to be more than one solution? Please help me

    Last edited by MichaelLight; February 20th 2011 at 02:39 AM.
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  2. #2
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    Quote Originally Posted by MichaelLight View Post
    Given α and β are the roots of the quadratic equation px^2+qx+r=0, find the relationship between p,q and r if

    a)
    α=2β+1
    b)
    α=3β+1

    Answers provided by the answer sheet are 2q^2 + pq - p^2 = 9pr and 3q^2 + 2pq - p^2 =16pr respectively.

    Can you help me?
    You should know that if \alpha and \beta are the roots of a quadratic equation, px^2+qx+r=0 then the relation between the coefficients and the roots are,

    \alpha+\beta=-\frac{q}{p}-----(1)

    \alpha\beta=\frac{r}{p}---------(2)

    If \alpha=2\beta+1--------(3)

    Using equations (1),(2) and (3) eliminate \alpha~and~\beta.

    Use the same method for part b).
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