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Math Help - Polynomial Functions Question Help (Urgent)

  1. #1
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    Polynomial Functions Question Help (Urgent)

    I just can't get this question and need some help:

    The equation 3x^3 + 25x^2 - 48x = -20 has roots of 1, h and k. Determine a quadratic equation f(x) whose roots are "h+k" and "hk". Present your final answer both in factored and expanded form.

    Thanks in advance ^_^
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  2. #2
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    Ok... Well, i might not even know how to do this problem, although i will give it a shot. I know the idea of what you have to do.

    Equation:

    3x^3\oplus25x^2\ominus48x\oplus20

    Here the objective is to factor this. This is what i shall attempt to do, you know that one of the roots is 1, so you plug that in automatically. I well get back to this post, and edit it, if i manage to factor this cubic -.- if i dont edit it, i didn't get it, and your on your own
    Last edited by rtblue; March 24th 2009 at 04:44 PM.
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  3. #3
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    Quote Originally Posted by Clueless View Post
    The equation 3x^3 + 25x^2 - 48x = -20 has roots of 1, h and k.
    Since one root is known, it can be divided out. So divide x - 1 from the polynomial 3x^3 + 25x^2 - 48x + 20.

    Apply the Quadratic Formula to the resulting quadratic factor to find the other two zeroes. Name one of them "h" and the other one "k".
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    Quote Originally Posted by stapel View Post
    Since one root is known, it can be divided out. So divide x - 1 from the polynomial 3x^3 + 25x^2 - 48x + 20.

    Apply the Quadratic Formula to the resulting quadratic factor to find the other two zeroes. Name one of them "h" and the other one "k".
    oh thanks I divided it and then forgot what to use

    So I got (x+1)(3x^2 + 22x - 70) - 50 = 3x^3 + 25x^2 - 48x + 20

    So all I need to do is use the quadratic formula on 3x^2 + 22x - 70? Also after that the rest of the question just wants me to get "hk" and "h+k" and replace them as roots?

    I'm not sure so just asking D:
    Last edited by Clueless; March 24th 2009 at 05:49 PM.
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  5. #5
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    Quote Originally Posted by Clueless View Post
    I got (x+1)(3x^2 + 22x - 70) - 50 = 3x^3 + 25x2 - 48x + 20
    How did you get this...?

    Note: Since you're being asked to factor, rather than to break into terms, you need to divide the x - 1 (not "x + 1", since x = -1 is not given as a zero) into the polynomial provided earlier.

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  6. #6
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    Quote Originally Posted by stapel View Post
    How did you get this...?

    Note: Since you're being asked to factor, rather than to break into terms, you need to divide the x - 1 (not "x + 1", since x = -1 is not given as a zero) into the polynomial provided earlier.

    I did synthetic division by negative 1 and got 3 , 22, -70 and also -50 as a remainder.

    Also that's my division statement. Tell me if I did it wrong and what exactly the right answer is T_T
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  7. #7
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    Quote Originally Posted by Clueless View Post
    I did synthetic division by negative 1 and got 3 , 22, -70 and also -50 as a remainder.

    Also that's my division statement. Tell me if I did it wrong and what exactly the right answer is T_T
    do synthetic division with 1. the root is x = 1, not -1.

    you should get 0 as the remainder, right?
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