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13 July, 23:12

Potential roots of p (x) = x^4 - 9x^2 - 4x + 12

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  1. 14 July, 00:38
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    -6, - 4, - 3, - 2, - 1, 1, 2, 3, 4, 6

    Step-by-step explanation:

    The general formula for a fourth-degree polynomial is

    f (x) = ax⁴ + bx³ + cx² + dx + e

    Your polynomial is

    f (x) = x⁴ - 9x² - 4x + 12

    a = 1; e = 12

    According to the Rational Roots Theorem, the possible rational roots are the factors of e divided by the factors of a.

    Factors of e = ±1, ±2, ±3, ±4, ±6

    Factors of a = ±1

    Potential roots are x = ±1 ±2, ±3, ±4 ± 6

    Putting them in order, we get the potential roots

    x = - 6, - 4, - 3, - 2, - 1, 1, 2, 3, 4, 6

    (The graph of your function shows roots at x = - 2, x = 1, and x = 3.)
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