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:
