How Do You Use Technology to Solve a Polynomial Equation?

Use a graphic display calculator (GDC) to enter the polynomial equation into a polynomial solver or graph it and find its zeros. Record the equation entered and give every required solution using mathematical notation, normally exactly or to three significant figures.

This is SL 1.8: Use of technology to solve polynomial equations, studied by both SL and HL students. It may appear on any Mathematics: Applications and Interpretation paper because a GDC is required on every paper.

Method 1: Polynomial Solver

Suppose you must solve

$$x^3-4x^2-x+4=0.$$

1. Rearrange the equation so that one side is zero.
2. Open the GDC's polynomial solver and select degree $3$.
3. Enter the coefficients in descending powers of $x$:

$$1,\ -4,\ -1,\ 4.$$

4. The calculator returns

$$x=-1,\quad x=1,\quad x=4.$$

These values are the roots or zeros of the polynomial.

To verify the result, substitute each root into the original polynomial or use a table. For example, at $x=4$, $4^3-4(4^2)-4+4=0$. A graph should also cross the -axis at , , and . Agreement between methods reduces data-entry errors, especially sign mistakes or an incorrect coefficient order.

A common misconception is that missing terms can be omitted from the coefficient list. They cannot: for $x^3-5x+2=0$, enter $1,0,-5,2$, including the zero coefficient of .

Exam Technique

Write the original equation and the solutions, not a sequence of calculator keystrokes. Check the viewing window if using a graph, include all roots in the required domain, retain full GDC precision during calculations, and round only the final answers. The IB does not require a particular algebraic method for SL 1.8, so correct use of technology is expected.