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    Polynomials : Zeros and Complex Roots

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    Find the polynomial f(x) of degree three that has zeroes at 1, 2, and
    4 such that f(0) = -16.
    a. f (x) = x3 − 7x2 +14x −16
    b . f (x) = 2x3 −14x 2 + 28x −16
    c . f (x) = 2x3 −14x 2 +14x −16
    d . f (x) = 2x3 + 7x2 +14x +16

    Find the third degree polynomial whose graph is shown in the figure.

    a. f (x) = x3 −x 2 −2x + 2
    b . 2
    2
    1
    4
    f (x) = 1 x3 − x 2 −x +
    c . 2 2
    4
    1
    4
    f (x) = 1 x3 − x 2 + x +
    d . 2
    2
    1
    2
    f (x) = 1 x3 + x 2 −x +

    The figure shows the graph of the polynomial function y = f(x). For
    which of the values k = 0, 1, 2, or 3 will the equation f(x) = k have
    complex roots?
    a. 0
    b . 1
    c . 2
    d . 3

    © BrainMass Inc. brainmass.com December 24, 2021, 6:32 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/polynomials-zeros-and-complex-roots-121326

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    Polynomials, zeros and complex roots are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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