### Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem11-103

11-103.

Sketch a graph, $y = f\left(x\right)$, 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 $x$-axis, so this graph should intersect the $x$-axis $5$ times.

1. Three real and two 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. 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).