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Math Help - Potential Rational Zeros

  1. #1
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    Potential Rational Zeros

    List the potential rational zeros of the polynomial function below. Do NOT attempt to find the zeros.

    f(x) = -6x^3 - x^2 + x + 10

    How do I make a list of such zeros?
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  2. #2
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    Use the Rational Root Test:
    The Rational Roots Test
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  3. #3
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    Quote Originally Posted by magentarita View Post
    List the potential rational zeros of the polynomial function below. Do NOT attempt to find the zeros.

    f(x) = -6x^3 - x^2 + x + 10

    How do I make a list of such zeros?
    Use the Rational Zeros Theorem:

    P: List all possible factors of leading coefficient (-6): -6, -3, -2, -1, 1, 2, 3, 6
    Q: List all possible factors of lone constant (10): -10, -5, -2, -1, 1, 2, 5, 10

    List all numbers \frac{P}{Q}, all possible solutions lie in the set

    I would find it much easier to do some factoring...

    f(x)=x(-6x^2-x+1)+10

    f(x)=x(2x+1)(-3x+1)+10

    To have f(x)=0, we need x(2x+1)(1-3x)=-10

    Let's try x = 1, this gives us -6
    x = 2 gives us -50

    Our answer must lie between 1 and 2, so what possible solutions, from the Rational Zeros theorem are between 1 and 2?

    \frac{5}{3}, \frac{6}{5}, \frac{3}{2}

    Can you finish this out now?

    =======================

    Is LaTeX not working for some reason?
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  4. #4
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    Fantastic!

    I thank you both, especially Colby for your detailed explanation.
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  5. #5
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    Quote Originally Posted by magentarita View Post
    List the potential rational zeros of the polynomial function below. Do NOT attempt to find the zeros.

    f(x) = -6x^3 - x^2 + x + 10

    How do I make a list of such zeros?
    The rational root theorem tells you that any rational root of a polynomial with integer coeficients is the ratio of a divisor (positive or negative) of the constant term to a divisor (positive or negative) of the coefficient of the highest order term.

    The divisors of -6 are +/- 1, +/- 2, +/- 3, +/- 6, and of 10 are +/- 1, +/-2, +/- 5 +/- 10.

    RonL
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  6. #6
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    Great math notes.

    Your replies are helping me more and more each day.
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