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Math Help - help please~

  1. #1
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    help please~

    ‘The quadratic equations (x^2)-6x+2k=0 and (x^2)-5x+k=0 have a common root A. (i.e. A is a root of both equations)
    Show that A=k and hence find the value(s) of k.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by stupid_kid View Post
    ‘The quadratic equations (x^2)-6x+2k=0 and (x^2)-5x+k=0 have a common root A. (i.e. A is a root of both equations)
    Show that A=k and hence find the value(s) of k.
    Let the roots of x^2-6x+2k=0 be A and mu, and the roots of x^2-5x+k=0 be A and lambda

    The sum of the roots of x^2-6x+2k=0:

    A+mu=6 ...(1)

    and the product of the roots is:

    A.mu=2k ...(2)

    The sum of the roots of x^2-5x+k=0:

    A+lambda=5 ...(3)

    and the product of the roots is:

    A.lambda=k ...(4).

    Divide (2) by (3) to get mu=2.lambda ...(5)

    Subtract (3) from (1) to get mu-lambda=1 ...(6)

    Substituting (5) into (6) gives lambda=1, so by (5) mu=2, and by (2) A=k.

    RonL
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