Question

A polynomial function has a root of -6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2, and a

root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about
the graph is true?
O The graph of the function is positive on (-6, -2).
O The graph of the function is negative on (-0, 0).
O The graph of the function is positive on (-2, 4).
O The graph of the function is negative on (4.co).

Answer 1

9514 1404 393

Answer:

(a) the graph is positive on (-6, -2)

Explanation:

The roots, left to right, are ...

-6, -2, 0, 4

The odd-multiplicity roots, where the sign changes, are ...

-6, -2, 4

The function is negative to the left of -6, and positive to the right of +4. It is positive on the interval (-6, -2) and negative on the intervals (-2, 0) and (0, 4).