# Knowledge Base

## Solution 10215: Polynomial Root Finder and Simultaneous Equation Solver App gives Unexpected Result for the TI-83/84 Plus, TI-89/TI-92/Voyage 200 and the TI-85/TI-86 families of the Graphing line of Calculators.

### Why do I receive unexpected complex results when using the Polynomial Root Finder and Simultaneous Equation Solver Application?

The following explains why complex results are given when using the Polynomial Root Finder and Simultaneous Equation Solver App for the TI-83 Plus family or TI-84 Plus family graphing calculator. (Note: This behavior also applies to the TI-89/TI-92 Plus/Voyage™ 200 Polynomial Root Finder Application and the TI-85/TI-86 Poly feature.)

Due to 14-bit calculation in the basecode, in some cases the results returned will contain an imaginary part (often small but sometimes significant) instead of a real-valued zero.

While using the App, press the MODE key to display the mode settings for Polynomial Root Finder and Simultaneous Equation Solver App. The mode screen will look very similar to the basecode settings. The default setting is REAL for display, hence showing NONREAL for any roots that contain imaginary parts.

Select the display mode to be a+bi, which will display the roots in a+bi format, such as 1+2i, etc.

Refer to the example problem below.

Example:

x^3 -3x^1 + 2 = 0

where a3 = 1, a2 = 0, a1 = -3, and a0 = 2.

The answer should be -2, 1, 1.

The Polynomial Root Finder and Simultaneous Equation Solver App displays an answer of x1 = -2, x2 = NONREAL, and x3 = NONREAL

Solution:

The PolySmlt application actually calculates the roots to be x1 = -2, x2 = 1+2.574..e-7i, x3 = 1-2.574..e-7i

For clarity without scientific notation this is x1=-2, x2=1+0.0000002574...i, x3=1-0.0000002574...i

For this example, if the calculator is in REAL mode, it can be confusing to see the answer as -2, NONREAL, NONREAL. But if the mode is selected to a+bi, it would make a little more sense.