### Home > A2C > Chapter 11 > Lesson 11.3.4 > Problem 11-172

11-172.

Sketch a graph, *f*(*x*), that has the numbers and types of roots for each situation described below.

5 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*x*-axis, so this graph should intersect the*x*-axis 5 times.

3 real and 2 complex roots

This polynomial has 5 roots, but only 3

*x*-intercepts.A possible graph would be a polynomial with 3

*x*-intercepts plus another bend.

4 complex roots

The degree of this polynomial is even, so it starts and ends in the same direction.

4 complex and 2 real roots

See parts (a), (b), and (c).