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Thread: Two problems

  1. #1 Two problems 
    Forum Freshman IAlexN's Avatar
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    For what value on "a" has the equation an infinite amount of solutions?

    For a quadratic polynomial:



    What is the polynomial p(x).

    I don't want the answers to these questions, I simply would like some help with them. As I don't know where to start with either of them.

    EDIT: I believe that I have managed to solve the first problem. I'd like to know if it's a valid solution.

    "[unparseable or potentially dangerous latex formula]"

    Hopefully this will suffice.

    (x^2+2x+1)^2 = (x+a)^4
    (x^2+2x+1) = (x+a)^2
    (x+1)^2 = (x+a)^2
    (x+1) = (x+a)
    1 = a


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  3. #2  
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    For the second problem you need to use a method call "synthetic division"

    http://www.purplemath.com/modules/synthdiv.htm

    http://mathworld.wolfram.com/SyntheticDivision.html

    Above are a couple of websites which give details. If you google "synthetic division" you can get a lot more.


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  4. #3  
    Forum Freshman IAlexN's Avatar
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    Quote Originally Posted by mathman
    For the second problem you need to use a method call "synthetic division"
    Thank you for your reply, and the links. I had a look at both the websites, but I'm not quite sure how to apply the method to the problem addressed in my question.
    When one person suffers from a delusion, it is called insanity. When many people suffer from a delusion it is called a Religion.

    Robert M. Pirsig
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  5. #4  
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    p(x)=(x^3 + x - 2)/(x - 1)

    Step 1a: x^2 = x^3/x
    Step 1b: (x^3 +x - 2)-x^2(x - 1) = x^2 + x - 2
    Step 2a: x=x^2/x
    Step 2b: (x^2 + x - 2) -x(x - 1)= 2x - 2 = 2(x-1)
    (I have elided the last step, because of the obvious factor of (x - 1).)

    Final answer p(x) = x^2 + x + 2
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