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Math Help - qu-quadratic eqn.

  1. #1
    Newbie magaski's Avatar
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    Smile qu-quadratic eqn.

    Find the value of p so that the equation x^2+10x+21=0 and x^2+9x+p=0 may have a common root. Find also the equation formed by the other root.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    Observe that f(x) = x^2+10x+21 = (x+3)(x+7). Hence roots of f(x) = 0 are x=-3 and x=-7.

    Observe that roots of g(x) = x^2+9x+p =0 are given by x_0 = \frac{-9\pm \sqrt{81-4p}}{2}.

    Thus if you find the values of p where x_0 = -3 or x_0 = -7 you're done.
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  3. #3
    Senior Member Dinkydoe's Avatar
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    Sorry. This can be done easier ;p.

    Since you must find p such that (x-a)(x+3) =x^2+(3-a)x-3a = x^2+9x+p. Observe the only possibility is a = -\frac{p}{3}.

    Thus now we must find p such that: x^2+(3+\frac{p}{3})x+ p= x^2+9x+p. This gives p = 18

    Now you can do the same trick for f(x) = (x-a)(x+7) to find another value of p
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