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


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

  1. 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.

  1. 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.

  1. 4 complex roots

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

  1. 4 complex and 2 real roots

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