Home > CCA2 > Chapter 11 > Lesson 11.3.1 > Problem11-95

11-95.

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

2. $4$ complex roots

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

2. $4$ complex and $2$ real roots

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