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25 August, 22:49

F (x) = 4x^3 + ... + 9

list all possible rational zeroes of the function

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  1. 26 August, 01:40
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    The Rational Root Theorem says any rational zeros of f must be a fraction with a factor of the constant (9 here) in the numerator and a factor of the leading coefficient (4 here) in the denominator. We have to include negative factors.

    Factors of 9: - 9, - 3, - 1, 1, 3, 9

    Factors of 4: 1, 2, 4

    We only have to consider negative numbers for the numerator to get all the possible values.

    We just make the list, going through all the numerators one denominator at a time.

    Possible rational zeros, i. e. possible rational values for x such that f (x) = 0 are

    Answer: - 9, - 3, - 1, 1, 3, 9, - 9/2, - 3/2, - 1/2, 1/2, 3/2, 9/2, - 9/4, - 3/4, - 1/4, 1/4, 3/4, 9/4
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