Question

The illustration below is a graph of the polynomial function P(x). The graph crosses the x-axis 2 times and touches the x-axis once at the point (4, 0).

Part A: Use the key features of the graph to explain that the degree of the polynomial cannot be odd.

Part B: How many unique zeros does this polynomial have?

Answer 1

The polynomial graph crosses the x-axis at two points and touches x-axis at one point. It indicates the graph has four roots:

$x=-1.5$
$x=-2$
$x=4$
$x=4$

The last two roots have equal value as the graph touches the x-axis (not crosses it)

The graph has three unique roots