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Math - Rational Roots

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1.) What are the possible rational roots of the function f(x) = 3x^4 - x - 2

2.) What are the rational roots of the following equation: x^3 - 4x^2 - 4x +16 = 0

Thank you for any help!

  • Math - Rational Roots - ,

    1. 4 possible.

    2. x = -2, 2, 4.

  • Math - Rational Roots - ,

    1. By the rule of Des Cartes, the coefficients changed signs once, so there is at least one real positive root, perhaps three.
    The fact that sum of the coefficients equals zero, indicate that (x-1) is a factor.
    Do a long division to reduce the polynomial to a cubic, and search for other rational roots, if there is any.
    The dominance of the 3x^4 term tells us that the graph would resemble that of 3x^4, displaced -2 downwards, hence there would likely to be a positive root and a negative root, and two complex roots.

    2. Factorize, if possible.

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