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).