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31 January, 13:11

A polynomial function has a root of - 5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true?

The graph of the function is positive on (-co, - 5).

The graph of the function is negative on (-5,3).

The graph of the function is positive on (-co, 1).

The graph of the function is negative on (3, co).

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Answers (2)
  1. 31 January, 13:52
    0
    It's the last one. And the first one ... It's negative on the interval (3, co) and positive on (-co,-5)
  2. 31 January, 16:18
    0
    Answer: The graph of the function is positive on (-co, - 5).

    The graph of the function is negative on (3, co).

    Step-by-step explanation:

    We know that the roots are in: - 5, 1 and 3.

    and after 3, the graph is in the negative side, so between 1 and 3 the graph must be in the positive side, between - 5 and 1 the graph must be in the negative side, and between - inifinity and - 5 the graph must be in the positive side:

    So the statements that are true are:

    The graph of the function is positive on (-co, - 5).

    The graph of the function is negative on (3, co).
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