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15 April, 10:24

According to the real rational root theorem, what are all the potential rational roots of f (x) = 5x3-7x+11

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  1. 15 April, 12:10
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    x = - 11, - 11/5, - 1, - 1/5, 1/5, 1, 11/5,11

    Step-by-step explanation:

    The general formula for a third-degree polynomial is

    f (x) = ax³ + bx² + cx + d

    Your polynomial is

    f (x) = 5x³ + 7x + 11

    a = 5; d = 11

    p/q = Factors of d/Factors of a

    Factors of d = ±1, ±11

    Factors of a = ±1, ±5

    Potential roots are x = ±1/1, ±1/5, ±11/1, ±11/5

    Putting them in order, we get the potential roots

    x = - 11, - 11/5, - 1, - 1/5, 1/5, 1, 11/5, 11

    (There are no rational roots. There is one irrational root and two imaginary roots.)
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