The points plotted below are on the graph of a polynomial. How many roots of the polynomial lie between x = -4 and x = 3?

Question

The points plotted below are on the graph of a polynomial. How many roots of the polynomial lie between x = -4 and x = 3?
http://media.apexlearning.com/Images/200708/27/2fc49438-d540-45ec-a35d-2ac331da9b56.gif

A. 4
B. 2
C. 1
D. 3

Answer 1

It looks like a graph of a 4th degree polynomial, in which case connecting adjacent points will show all of the zero crossings. There are four.



However, there are enough points given to define a 12th degree polynomial. These may have more zero-crossings in the interval of interest. Here is a 10th degree polynomial through these points with six zero crossings. The question is badly worded, and the answer set given does not allow for all of the possibilities.

Answer 2

Consider what the root of a polynomial is, it's a point x where p(x) = 0.



In terms of the graph then, it's a point which lies on the line p(x) = 0, or y = 0, or just the x-axis.



From the graph, there is one such point lying on the x-axis, so the answer is C.

Answer 3

Imagine a smooth curve going thru all those points --- it would cross the x axis 4 times --- so there are roots