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Math Help - mixed bag part 1:assessing parabolas, and binomial expansions

  1. #1
    Member MathBlaster47's Avatar
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    mixed bag part 1:assessing parabolas, and binomial expansions

    Some mixed questions I need some confirmation on.

    1:
    Find (a) the directrix, (b) the focus and (c) the roots of the parabola y=x^2-5x+4.

    I can find the directrix and the focus no problem, but i do not understand what they mean by "roots". Do they mean the roots(positive and negative) of the equation or something else?

    2:
    Write the first three terms of the expansion of (a-b)^{10}.

    Answer:
    a^{10}+10a^9b-45a^8b^2

    3:
    What are the last three terms of (a-b)^7?

    Answer:
    21a^2b^5+7ab^6-b^7

    Thank you!
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by MathBlaster47 View Post
    Some mixed questions I need some confirmation on.

    1:
    Find (a) the directrix, (b) the focus and (c) the roots of the parabola y=x^2-5x+4.

    I can find the directrix and the focus no problem, but i do not understand what they mean by "roots". Do they mean the roots(positive and negative) of the equation or something else?

    "roots" are the solutions to \textcolor{red}{x^2-5x+4 = 0}

    2:
    Write the first three terms of the expansion of (a-b)^{10}.

    Answer: a^{10}+10a^9b-45a^8b^2

    sign errors ...

    a^{10}\textcolor{red}{-}10a^9b\textcolor{red}{+}45a^8b^2



    3:
    What are the last three terms of (a-b)^7?

    Answer:
    21a^2b^5+7ab^6-b^7

    one sign error

    Thank you!
    ...
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  3. #3
    Member MathBlaster47's Avatar
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    Quote Originally Posted by skeeter View Post
    Quote Originally Posted by MathBlaster47 View Post
    Some mixed questions I need some confirmation on.

    1:
    Find (a) the directrix, (b) the focus and (c) the roots of the parabola y=x^2-5x+4.

    I can find the directrix and the focus no problem, but i do not understand what they mean by "roots". Do they mean the roots(positive and negative) of the equation or something else?

    "roots" are the solutions to

    2:
    Write the first three terms of the expansion of (a-b)^{10}.

    Answer:
    a^{10}+10a^9b-45a^8b^2


    sign errors ...






    3:
    What are the last three terms of (a-b)^7?

    Answer:
    21a^2b^5+7ab^6-b^7

    one sign error

    Thank you!
    ...
    I thought that might have been what they meant by roots, I just wasn't quite sure--I thought I might have been confusing my terms or something....

    Dang....sign error....live and learn...

    For 3 it's supposed to be:
    [tex]21a^2b^5-7ab^6+b^7[\math]?


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  4. #4
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    Quote Originally Posted by MathBlaster47 View Post

    For 3 it's supposed to be:
    21a^2b^5-7ab^6+b^7?

    I said one sign error ... try again.
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  5. #5
    Member MathBlaster47's Avatar
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    Quote Originally Posted by skeeter View Post
    I said one sign error ... try again.
    So not:
    21a^2b^5-7ab^6+b^7
    But:
    21a^2b^5-7ab^6-b^7

    I'm trying my best not to guess, so I charted it out. The only confusing thing is which sign to start with--since its odd though, I figure that it will finish with a different sign than it started.
    Last edited by MathBlaster47; February 27th 2010 at 10:40 AM.
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