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Thread: Roots of a Quadratic equation

  1. #1
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    Roots of a Quadratic equation

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

    a)Prove that $\displaystyle 2L^2=9M$

    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 $\displaystyle x^2+Lx+M$ has one root which is twice the other.

    a)Prove that $\displaystyle 2L^2=9M$

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

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

    So either $\displaystyle r_1=2r_2$ or $\displaystyle r_2=2r_1$ 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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