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Math Help - Zeros of Cubic Poly and Inverse Funct.

  1. #1
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    Zeros of Cubic Poly and Inverse Funct.

    I'm trying to find all zeros by either factoring and/or using the quad. formula for:

    f(x) x^3 - 2x^2 - x + 2

    Next, I'm trying to show that f(g((x)) = x and g(f(x)) = x for all x:

    f(x) = 2x^3 + 1 or g(x) = [cube root] (x-1/2)

    Thanks in advance for any help


    Just figured out both problems. Thanks for all the help!
    Last edited by toop; January 19th 2008 at 12:13 PM.
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  2. #2
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    I'm trying to find all zeros by either factoring and/or using the quad. formula for:

    f(x)= x^{3} - 2x^{2} - x + 2
    You could try the Rational Root Theorem. Try x=2 as a root.

    That is, divide \frac{x^{3}-2x^{2}-x+2}{x-2}. If it reduces to a quadratic, then 2 is a factor and the quadratic is easily solved for the other two factors.
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  3. #3
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    Awesome, I came up with 1, -1, and 2. Seems like a reasonable answer to me....thanks
    Last edited by toop; January 19th 2008 at 12:10 PM.
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  4. #4
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    Hello, toop!

    Find all the zeros of: . f(x) \:x\:^3 - 2x^2 - x + 2

    Factor "by grouping": . x^2(x-2) - (x-2) \;=\;0

    Factor: . (x-2)(x^2-1)\;=\;0\quad\Rightarrow\quad (x-2)(x-1)(x+1)\;=\;0

    Therefore: . x \;=\;2.\:1,\:-1

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  5. #5
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    Thanks again!
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