Method Two: Solve x2 - 4x + 1 = 0, then test chosen values
Solve x2 - 4x + 1 = 0

x2 - 4x + 1 = 0                                  Solve by using the quadratic formula

Solve by using the Quadratic Formula

Graph of the solution to the quadratic EQUATION

Choose test values

Choose "test" values that do not belong to the solution set of x2 - 4x + 1 = 0, but are representative of each "region" determined by the solution set. Substitute the chosen values into the quadratic inequality to see which values yield a TRUE result.


For example, choose the test values 0, 2 and 4.


Choose representatice test values

Substitute the test values into the original quadratic inequality (x2 - 4x + 1 > 0) to see which values yield a true result.

Test each chosen values

Since 2 results in a FALSE statement, the region it represents are NOT part of the solution set of the inequality.


Since 0 and 4 result in TRUE statements, the regions they represent ARE part of the solution set of the inequality.


Solution Set
Solution set to the original inequality