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Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem 11-103


Sketch a graph, , that has the number and types of roots described for each situation below.

  1. 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.

  1. 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.

  1. Four complex roots

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

  1. Four complex and two real roots

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