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Math Help - Please Help me about integral expression >_<

  1. #1
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    Please Help me about integral expression >_<

    My teacher gave us a problem and I cannot understand how did she do it >_< it is about integral expression I am really weak at mathematics even I focus it takes time for me to understand the topic but she is very fast when teaching I hope you can help me I didn't even have any idea what is integral expression she gave us this problem
    consider the integral expression in x
    P=x^3 + x^2 + ax + 1
    where a is a rational number, At a=? the value of P is a rational number for any x which satisfies the equation x^2 + 2x -2=0, and in this case the value of P =?
    and the answer is a=-4 p=-1
    how she do it and what is integral expression I am very sorry >_<
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  2. #2
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    Re: Please Help me about integral expression >_<

    Find the roots of x^2 + 2x - 2 = 0, substitute them into x^3 + x^2 + ax + 1 and see when the resulting expression of a is rational.
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  3. #3
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    Re: Please Help me about integral expression >_<

    thank you but where did you get x^2 + 2x -2 = 0?
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  4. #4
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    Re: Please Help me about integral expression >_<

    Quote Originally Posted by sarcosuchus View Post
    thank you but where did you get x^2 + 2x -2 = 0?
    Hmm, have you fully read the text of the problem?
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  5. #5
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    Re: Please Help me about integral expression >_<

    Quote Originally Posted by sarcosuchus View Post
    My teacher ... but she is very fast when teaching...
    ....the equation x^2 + 2x -2=0,
    You seem to be "very fast" when reading...
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  6. #6
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    Re: Please Help me about integral expression >_<

    Quote Originally Posted by sarcosuchus View Post
    thank you but where did you get x^2 + 2x -2 = 0?
    The point is that you said, in the problem, "for any x which satisfies the equation x^2 + 2x -2=0". That's where emakarov got it!
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  7. #7
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    Re: Please Help me about integral expression >_<

    oh thank you I didn't noticed it since I am always focus at the first given problem >_<
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    Re: Please Help me about integral expression >_<

    Quote Originally Posted by sarcosuchus View Post
    At a=? the value of P is a rational number for any x which satisfies the equation x^2 + 2x -2=0,
    Huh? Sure was part of the given problem...
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