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Math Help - Can you... Prove that

  1. #1
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    Can you... Prove that

    Hello all, wondering if you could give me a hand,

    Prove that the equation 4=x(2-x) has no real roots.

    Thanks in advance,

    Max
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  2. #2
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    Expand, move everything to one side, so that you have a quadratic of the form ax^2 + bx + c = 0.

    Then check the discriminant. If the discriminant is negative, then there are not any real roots.
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  3. #3
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    Thanks a lot, I get it now.

    Max
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  4. #4
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    Quote Originally Posted by Max888 View Post
    Hello all, wondering if you could give me a hand,

    Prove that the equation 4=x(2-x) has no real roots.

    Thanks in advance,

    Max
    Alternatively, here's how Fred Flinstone might have done it...

    4=x(2-x)

    x(x-2)=-4

    (a\ number)(a\ value\ 2\ less\ than\ that\ number)=-4

    1(-1)=-1

    To get a -4, we need a +4 instead of 1

    or a -4 instead of -1

    Apart from those, we need (2)(-2) or (-3.?)(1.?)

    or (-1.?)(3.?)

    or (4.?)(-0.?) etc, etc none of which can differ by 2

    Much quicker to know the "abc" formula.
    Last edited by Archie Meade; July 14th 2010 at 01:17 PM.
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  5. #5
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    Right, thanks a lot!
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