Question

3. Stanley analyzes the table of values for a polynomial function. He has determined through applying Descartes’ rule of sign that there is 1 negative real zero, and either 1 or 3 positive real zeros. He has also determined that the upper bound of the function is 3.

Answer 1

Answer:

A. The degree of the function is at least 4

B. At least 3 positive real zeros

Step-by-step explanation:

From the table we can see that the value of the polynomial function is first negative, then positive (1 intersection with x-axis), then again negative (second intersection with x-axis), then again positive (third intersection with x-axis), and at last again negative (fourth intersection with x-axis).

The point of intersection with x-axis corresponds to the zero of the function (f(x)=0). Since the graph of the function intersects 4 times the x-axis, the degree of the polynomial function is at least 4.

the first point of intersection with x-axis has negative x-coordinate. All other points have positive x-coordinates. This means the function has zt least 3 positive real zeros.