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Math Help - How do I do this?

  1. #1
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    How do I do this?

    Find all real and imaginary zeros of f(x) = x^3 + x^2 + 13x - 15, given that 1 is a zero of the function.

    Would I use synthetic division? If so, how?

    Any help is appreciated.
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  2. #2
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    Quote Originally Posted by iluvmathbutitshard View Post
    Find all real and imaginary zeros of f(x) = x^3 + x^2 + 13x - 15, given that 1 is a zero of the function.

    Would I use synthetic division? If so, how?

    Any help is appreciated.
    you have f(1)=0 which means (x-1) is a factor.
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  3. #3
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    ok, so I would use that for synthetic division?

    Thank you for answering
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  4. #4
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    Quote Originally Posted by iluvmathbutitshard View Post
    ok, so I would use that for synthetic division?

    Thank you for answering
    i believe yes.
    divide x^3+x^2+13x-15 by x-1.
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  5. #5
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    Ok, so when I divided I got x^2 + 2x + 15?
    How are these zeros?
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  6. #6
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    Quote Originally Posted by iluvmathbutitshard View Post
    Ok, so when I divided I got x^2 + 2x + 15?
    How are these zeros?
    use the ABC formula to find the roots
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  7. #7
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    Quote Originally Posted by iluvmathbutitshard View Post
    Ok, so when I divided I got x^2 + 2x + 15?
    How are these zeros?
    "They" aren't zeros. The zeros of the original polynomial are 1 and the zeros of this quadratic polynomial. Solve x^2+ 2x+ 15= 0 by completing the square or the quadratic equation.
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  8. #8
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    x^3 + x^2 + 13x - 15=(x-1)(x^2 + 2x + 15)=(x-1)((x+1)^2+14).
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  9. #9
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    The imaginary zeros are obtained from x^2+2x+15,
    since this factor of the cubic does not itself have real factors,
    it has complex factors since b^2<4ac.
    x^2+2x+15 is zero for x = {-2+sqrt(4-60)}/2
    and for x = {-2-sqrt(4-60)}/2,
    which are x = -1+i(sqrt[14]) and x = -1-i(sqrt[14]).
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