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Math Help - Determining all the zeros of a function

  1. #1
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    Determining all the zeros of a function

    Determine the zero's


    f(x) = kx^3 - 8x -x +3k + 1 k=3 and has a zero when x = 2


    3x^3 - 8x^2 - x + 3(3) + 1

    = 3x^3 - 8x^2 - x +10 <<<<< don't know what to do after this step
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  2. #2
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    Quote Originally Posted by Devi09 View Post
    ...
    It's hard to follow what you did: what happened to k?
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  3. #3
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    Well you had to first find the value of k which is 3 after you solve for it given one of the zeros which was 2
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  4. #4
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    You probably have to factor 3x^3 - 8x^2 - x +10 to get the zeros. But Im stuck at that part
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  5. #5
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    Quote Originally Posted by Devi09 View Post
    You probably have to factor 3x^3 - 8x^2 - x +10 to get the zeros. But Im stuck at that part
    You know that x=2 is a root, so (x-2) is a factor. So divide 3x^3 - 8x^2 - x +10 by (x-2) to get the quadratic which will give you the two remaining roots.

    CB
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  6. #6
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    Hello, Devi09!

    \text{Determine the zeros:}

    . . <br />
f(x) \:=\: kx^3 - 8x^2 -x +3k + 1,\;k=3
    Why do they do that? . . . Can't they plug in the 3?

    . . \text{and has a zero when }x = 2.

    So we have: . f(x) \:=\:3x^3 - 8x^2 - x + 10

    Since f(2) = 0, then (x\!-\!2) is a factor of \,f(x).

    We find that: . f(x) \;=\;(x-2)(3x^2-2x-5) \;=\;(x-2)(x+1)(3x-5)


    Therefore, the zeros are: . x\:=\:2,\,\text{-}1,\,\frac{5}{3}


    Edit: Too slow . . . again.
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