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Math Help - discriminant

  1. #1
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    discriminant

    prove algebraically that no portion of the curve y=\frac{(a-x)^2}{2-x} exists for 0<y<4a-8
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    f(x)=y\Leftrightarrow \ldots \Leftrightarrow x^2+(-2a+y)x+a^2-2y=0


    There exists x iff

    \Delta=\ldots=y(y+8-4a)\geq 0

    Now, you can conclude.
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  3. #3
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    Quote Originally Posted by FernandoRevilla View Post
    f(x)=y\Leftrightarrow \ldots \Leftrightarrow x^2+(-2a+y)x+a^2-2y=0


    There exists x iff

    \Delta=\ldots=y(y+8-4a)\geq 0

    Now, you can conclude.
    b^2-4ac<0,

    (-2a+y)^2-4(1)(a^2-2y)<0
    y^2-4ay+8y<0
    y(y-4a+8)<0

    y<0 or y<4a-8
    but this does not tally with the one in the question
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    (y>0)\;\wedge\;(y<4a-8)\Rightarrow (y>0)\;\wedge\;(y-4a+8)<0\Rightarrow \Delta<0
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