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Math Help - [SOLVED] How to solve this question? Many thanks!

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    [SOLVED] How to solve this question? Many thanks!

    Given that \text{P(x)}\,\equiv{x^4 + x^3 + ax^2 + bx + c} where a, b, c are constants. If P(x) \equiv{(x - 1)^2 Q(x)}, Q(x) is a polynomial with integer coefficient and P(0) = 2, find the values of a, b, and c.


    The answer they gave is a = -3, b = -1 and c = 2 not a=-5, b=3
    Last edited by mr fantastic; June 5th 2009 at 05:12 PM. Reason: Merged posts and minor editing
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  2. #2
    MHF Contributor alexmahone's Avatar
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    P(0)=2
    c=2

    P(1)=0 (Why?)
    1+1+a+b+c=0
    a+b+4=0
    a+b=-4----(1)

    P'(1)=0 (Because x=1 is a repeated root)
    4+3+2a+b=0
    7+2a+b=0
    2a+b=-7-----(2)

    Solving (1) and (2),
    a=-3
    b=-1

    a=-3, b=-1, c=2
    Last edited by alexmahone; June 4th 2009 at 07:26 PM.
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    Hey, what does P' means and how do you do it? Why do you put the power of 4, 3 and 2 equals to 0? thanks!
    Last edited by mark1950; June 5th 2009 at 12:07 AM.
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    Member great_math's Avatar
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    Quote Originally Posted by mark1950 View Post
    Hey, what does P' means and how do you do it? Why do you put the power of 4, 3 and 2 equals to 0? thanks!
    P'(x) is the differentiated polynomial of P(x)<br />

    P'(x)=4x^3+3x^2+2ax+b

    P'(1)=0 because 1 is a repeated root of P(x) , so it must be a root of P'(x)

    and P(1)=0 because 1 is a root of P(x)
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  5. #5
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    Oh! Silly me. I've forgotten that the apostrophe sign was also a sign for differentiation. Thanks great math!
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