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Math Help - Perfect square root of a quadratic

  1. #1
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    Perfect square root of a quadratic

    Is it possible to find analytically the function that forms the perfect square root of a quadratic in all cases?

    For example with the quadratic x^2 + 10x + 25 you can find by factoring the perfect root x + 5. But how do you find the square root when a quadratic isn't expressed in the form of the completed square?

    With the quadratic x^2 + 10x + 20 it seems the simplest form you can get the root into is sqrt((x+5)^2 -5)).

    Is that the best that can be done? Is there some other way to express this root?
    Last edited by PaulMadroney; October 12th 2010 at 03:14 AM.
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  2. #2
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    I really cannot make heads or tails out of what you are saying. Either a quadratic is a perfect square or it is not. You cannot change a quadratic that is not a perfect square to a different "form" in which it is a perfect square. And I have no idea why you would prefer \sqrt{(x+ 5)^2- 5} to simply \sqrt{x^2+ 10x+ 20}. They both are "the function that forms the perfect square root of a quadratic".
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    I really cannot make heads or tails out of what you are saying. Either a quadratic is a perfect square or it is not. You cannot change a quadratic that is not a perfect square to a different "form" in which it is a perfect square. And I have no idea why you would prefer \sqrt{(x+ 5)^2- 5} to simply \sqrt{x^2+ 10x+ 20}. They both are "the function that forms the perfect square root of a quadratic".
    I see. I ask such a strange question because I have a calculation in which a square rooted quadratic results for each step and x is unknown at the time of the calculation. It seems I will have to store the complete series eg. \sqrt{5.123x^2 + 10.235x + 20.8} + \sqrt{2x^2 + 4.234x + 13.35} + ... whereas I was mistakenly thinking I would be able to simplify terms together. Thanks for your reply.
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