**Assignment 3**

**Investigation of ax² + bx+ c in the xb plane**

**by Venessa Brown**

The goal of this assignment is to explore the equation x² + bx + 1 = 0 in the xb plane.

How do we obtain the graph of equation x² + bx + 1 = 0 in the xb plane?

1. First solve the equation for b.

2. Replace b with y and graph.

Which is x² + yx + 1 = 0

Evaluating the roots of the equation x² + yx + 1 = 0 using the quadratic formula (keep in mind that y = b).

Notice that the we can have either two roots, one root, or no root to the equation depending on the outcome of the value of y² - 4.

Two roots:

One solution:

No Solution:

Consider the case when c = -1 instead of 1

Graph:

Roots of the equation when c is -1: