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Math Help - please help!! x^3 + ax^2 + bx+ c

  1. #1
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    Exclamation please help!! x^3 + ax^2 + bx+ c

    Hi
    so I am a student of Maths and Physics Track in my school
    And in todays class in Maths, the teacher gave us a question. And when no one could solve it, he said that there is going to be a quiz in it tomorrow
    I tried to solve it several times but I couldn't solve it

    anyways,, the question is



    if :: x^3 + ax^2 + bx + c
    the rest of dividing it on (x-1) is :: 4
    the rest of dividing it on (x+1) is :: -1

    find :: a , b , c
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  2. #2
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    Re: please help!! x^3 + ax^2 + bx+ c

    please help!! x^3 + ax^2 + bx+ c-3xfbl.png

    please right the way of solving it
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  3. #3
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    Re: please help!! x^3 + ax^2 + bx+ c

    The remainder when polynomial f(x) is divided by x-a is f(a). Considering this you get a+b+c = 3 abd a-b+c = 0. So b = 3/2 and a+c = 3/2. You can only have the solution in that form unless you have more information about the concerned polynomial.
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  4. #4
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    Re: please help!! x^3 + ax^2 + bx+ c

    by (x-a) you mean (x-1) ?!
    because i didnt get it
    and no i dont have more information
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  5. #5
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    Re: please help!! x^3 + ax^2 + bx+ c

    wait ... i got it
    but how did the 3 appeared ?!
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  6. #6
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    Re: please help!! x^3 + ax^2 + bx+ c

    can u explain more please
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  7. #7
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    Re: please help!! x^3 + ax^2 + bx+ c

    The remark of the remainder of f(x) being f(a) when divided by x-a is the statement of the remainder theorem, and the letter a is not the coefficient a of your problem here. The 3 appeared because f(1) = 4 implies 1+a+b+c = 4 which implies a+b+c = 3.
    Last edited by TheSaviour; March 5th 2012 at 03:21 PM.
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  8. #8
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    Re: please help!! x^3 + ax^2 + bx+ c

    and the b=3/2 ?!
    because if i only know this point
    i will solve it
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  9. #9
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    Re: please help!! x^3 + ax^2 + bx+ c

    do u mean
    when we have a positive B and a negative B
    we count them as 2B
    and to find B
    we make this 0+3
    so it will be like
    2B = 3
    B = 3/2
    ??
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  10. #10
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    Re: please help!! x^3 + ax^2 + bx+ c

    i've solved it
    thank you
    u saved my life
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  11. #11
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    Re: please help!! x^3 + ax^2 + bx+ c

    a = -2.5
    b = 1.5
    c = 4
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  12. #12
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    Re: please help!! x^3 + ax^2 + bx+ c

    I'm glad I was of help.

    Quote Originally Posted by Multi View Post
    do u mean
    when we have a positive B and a negative B
    we count them as 2B
    and to find B
    we make this 0+3
    so it will be like
    2B = 3
    B = 3/2
    ??
    Yes, you subtract the two equations from one another:

    a+b+c = 3
    a-b+c = 0
    ----------
    2b = 3

    => b = 3/2.

    a = -2.5
    b = 1.5
    c = 4
    Yes, that works, but so does (a, b, c) = (1, 3/2, 1/2) and many/infinite others. In fact, any a, c ∈ ℝ such that a+c = 3/2 works.
    I would leave it in the general form unless the teacher asked only for a pair or you have more restrictions on the given polynomial.
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