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Math Help - Unknown roots of two quadratics

  1. #1
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    Unknown roots of two quadratics

    Let (a, c) and (b, d) be the roots of the equation x^2 + ax - b = 0 and x^2 + cx + d = 0 respectively. Find all possible real values for a, b, c, d

    I'm not sure how to do this question and not sure how to approach it.

    Please help, BG
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  2. #2
    Moo
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    Hello,

    In a quadratic equation x^2+mx+n=0, m is the sum of the roots, and n is the product of the roots.

    So from the second equation, we have bd=d (1). And c=b+d (2)
    And from the first one, we have ac=-b (3) and a+c=a (4)

    From (4), we get c=0
    Substituting in (3), we get b=0
    Substituting in (1), we get d=0

    Then, a can take any values you want...
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