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Math Help - How to find the zeros of this function

  1. #1
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    How to find the zeros of this function

    Find all the zeros of the function and write the polynomial as a product of linear factors.
    f(x) = x^3 + 11x^2 + 39x + 29.

    So I think that I might need to use synthetic division, but I'm not sure. The teacher didn't explian this to me. Any help?
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  2. #2
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    Quote Originally Posted by tsmith View Post
    Find all the zeros of the function and write the polynomial as a product of linear factors.
    f(x) = x^3 + 11x^2 + 39x + 29.

    So I think that I might need to use synthetic division, but I'm not sure. The teacher didn't explian this to me. Any help?

    HI

    Factorise f(x) , do you know how ?

    f(x)=(x+1)(x^2+10x+29)

    x^2+10x+29 is complex , you can always check its discriminant .

    x+1 is a factor because f(-1)=0

    Then you can do the long division to get its quadratic factor .

    So the zero of this polynomial would be -1 because -1 makes f(x)=0
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  3. #3
    Senior Member pacman's Avatar
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    [I]factor: x^3 + 11x^2 + 39x + 29 = (x + 1)(x^2 + 10x + 29) = (x + 1)(x + (5 - 2i))(x + (5 + 2i))
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