Sketch a graph,
Five real roots
Since the degree is an odd number, it will start and end in different directions.
A real root occurs when the polynomial intersects the
-axis, so this graph should intersect the -axis times.
Three real and two complex roots
This polynomial has
roots, but only -intercepts.
A possible graph would be a polynomial with
-intercepts plus another bend.
Four complex roots
The degree of this polynomial is even, so it starts and ends in the same direction.
Four complex and two real roots
See part (a), (b), and (c).