Question

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 (-0, 5).
The graph of the function is negative on (-5, 3)
The graph of the function is positive on (-0, 1).
The graph of the function is negative on (3,co)
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Sabem

Answer 1

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

Explanation:

The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.

The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:

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