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Math Help - [SOLVED] Algebra: Please help!

  1. #1
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    Post [SOLVED] Algebra: Please help!

    Choose the statement that is true about the given quantities.

    Selection A:
    The number of rational zeros of f(x)=x^3 + 2x^2 - 11x -12.

    Selection B:
    The number of rational zeros of f(x)=x^3 - 8x^2 +16x +25.

    A)The two quantities are equal.
    B)The quantity in Selection A is greater.
    C)The quantity in Selection B is greater.
    D)The relationship cannot be determined from the given information
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by MR FRESH View Post
    Choose the statement that is true about the given quantities.

    Selection A:
    The number of rational zeros of f(x)=x^3 + 2x^2 - 11x -12.

    Selection B:
    The number of rational zeros of f(x)=x^3 - 8x^2 +16x +25.


    A)The two quantities are equal.
    B)The quantity in Selection A is greater.
    C)The quantity in Selection B is greater.
    D)The relationship cannot be determined from the given information
    To test if a is true set the two equal to each other and see what happens. This will also tell you which one's greater.
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  3. #3
    MHF Contributor

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    By the "rational root theorem", any rational root of a_nx^n+ a_{n-1}x^{n-1}+ \cdot\cdot\cdot+ a_1x+ a_0= 0, m/n, must have m a divisor of a_0 and n a divisor of a_n.

    In the first equation, a_n= a_3= 1 and a_0= -12 so any rational root must divide -12. What are the divisors of -12? How many of them actually satisfy the equation?

    In the second equation, a_n= a_3= 1 and a_0= 25 so any rational root must divide 25. What are the divisors of 25? How many of them actually satisfy the equation?
    Last edited by mr fantastic; June 30th 2009 at 02:30 PM. Reason: Moved from another thread
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