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Math Help - Roots of a Quadratic equation

  1. #1
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    Roots of a Quadratic equation

    The quadratic equation x^2+Lx+M has one root which is twice the other.

    a)Prove that 2L^2=9M

    b)Prove also that the roots are rational whenever L is rational
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by deltaxray View Post
    The quadratic equation x^2+Lx+M has one root which is twice the other.

    a)Prove that 2L^2=9M

    b)Prove also that the roots are rational whenever L is rational
    First the roots are:

    r_1=\frac{-L+\sqrt{L^2-4M}}{2} and r_2=\frac{-L-\sqrt{L^2-4M}}{2}

    So either r_1=2r_2 or r_2=2r_1 one of these has complex roots so is impossible for this problem, and the other should lead to the required solution.

    CB
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