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 (-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).

Answer 1

It’s the last one. And the first one... It’s negative on the interval (3,co) and positive on (-co,-5)

Answer 2

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

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

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).