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Math Help - System of Quadratic Inequalities.

  1. #1
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    System of Quadratic Inequalities.

    Sketch the intersection of the given inequalities. 1 y≥x^2 and 2 y≤-x^2+2x+4

    I can do this. You get a region of overlap, which is where the solution lies. My question is, this is a bounded region, but would we still say there are infinitely many solutions since, for instance, we can take x=0, x=0.1, x=0.01, x=0.001, x=0.0001 etc...that is, we can just move to another point in the region that is such a small difference over? Or since the region is bounded, is the solution set finite?

    Also,

    can you get a system of quadratic inequalities with all real numbers as the solution set? I know you can if the inequalities are just multiples of one another, but is there another way?
    Last edited by mr fantastic; November 20th 2011 at 02:40 AM. Reason: Title.
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  2. #2
    MHF Contributor Amer's Avatar
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    Re: System of Quadratic Inequalities.

    sure the solution is not finite as you know any interval (a,b) is not finite for b>a

    can you get a system of quadratic inequalities with all real numbers as the solution set? I know you can if the inequalities are just multiples of one another, but is there another way?
    I think you are talking about x values if so
    you can take y < x^2 , and y> -x^2 -1
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