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

11-172.
  1. Sketch a graph, f(x), that has the numbers and types of roots for each situation described below. Homework Help ✎

    1. 5 real roots

    2. 3 real and 2 complex roots

    3. 4 complex roots

    4. 4 complex and 2 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.

This polynomial has 5 roots, but only 3 x-intercepts.

A possible graph would be a polynomial with 3 x-intercepts plus another bend.

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

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