Using the TI-84 to solve equations

By Wednesday, November 30, 2016 , , , , 0

You must have a graphic display calculator (GDC). For HL and SL exams the GDC can only be used in Paper 2, but you will require it for both papers if you are following the Studies course. But don’t wait until the exams are close before practising the GDC functionality: you need to do this throughout the course so that you can use it to maximum effect in the exams.

Whatever level you are taking, it is almost inevitable that you will need to use your GDC to solve an equation or two. There are several ways this can be done and this blog takes you through the various methods, assuming you are using a TI-84. Unless I specify otherwise, all equations must be of the form f(x) = 0; if necessary, rearrange your equation to get zero on the right hand side.

1.   Using the PolySmlt APP

(If PolySmlt isn’t listed in the APPs, follow these download instructions to get hold of it)

“Poly” stands for polynomial equations, that is any equation of the form a + bx + cx2+dx3 + …. = 0. “Smlt” stands for simultaneous equations, which I’m not covering here.

When you select PolySmlt, you will first be asked to enter the degree of the equation, which is the highest power of x. Press ENTER, and then enter the coefficients. The screenshot shows the entry for x3 – 4x2 + 2x + 4 = 0. The options at the bottom of the screen can be selected using the keys just below. So, to solve the equation, press the GRAPH button.

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The solutions are then given. The big advantage of this method is that you get all the solutions at once, which you won’t get using any other method – but not all equations, of course, are of this form.

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2.    Using a graph

The easiest way to use a graph is to set the equation to f(x) = 0, draw the graph of f(x), and use the CALC options to find where the graph cuts the x-axis. For example, to solve x(2x – 3) = 0, first draw the graph of yx(2x – 3)

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We can see there are two solutions (one of them about x = 0, the other about
x = 2) because the graph intersects the x-axis in two places. To find these intercepts, select 2nd CALC, and then option 2:Zero. Since the calculator doesn’t know which zero you want, it asks you to give a left and a right bound: this can be done either by typing numbers (for example 1 and then 3 for the solution near x = 2), or by using the left and right arrows to move the cursor, pressing ENTER to set each bound. At this stage, the screen looks like this:

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You’re now asked to provide a “guess” which seems superfluous to me, but it has to be done. I usually just press the ENTER key. The solution comes up as 1.584….

If you need more solutions, repeat the process by selecting 2nd CALC again.

One word of warning. This method will not work if the solution is off the visible scale. For example, if the solution here was greater than x = 10, you would have created an error when trying to set the right bound.

You can also use graphs to solve an equation such as 2x – 3 = 4 – x2. Draw both graphs, and then use CALC option 5:intersect to find where the two graphs intersect.

3.    Using the built-in solver

Select the MATH menu, option B:Solver. Using this for the first time you get a screen headed EQUATION SOLVER. But the next time you use it, it will show the previous equation you solved – press the up arrow to get the solver screen.

Next to eqn:0= you must type in your function, for example x(2x – 3) as in the previous example, and press ENTER. The next bit is confusing, and you must be careful; see the screenshot:

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It looks as if the solution is 2.548, but this is the solution from the last time I used the Solver. In the second row you must type a guess (generally 1 works!) and immediately press ALPHA SOLVE. The solution will then appear (note the little black squares: if they aren’t there, you haven’t yet asked for a solution).

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You can ignore the lines below the solution. If there is more than one solution, go back to the X= line and repeat the procedure using a different guess.

4.    Using the SOLVE function

Ever pressed the CATALOG key? Here, you can find all the calculator functions, including dozens for which there is no key press. One of these is SOLVE (press S, which is the LN key, and then scroll down). Once selected, put the function, followed by an X, followed by your guess (all separated by commas), close the bracket and press ENTER. For example, to solve x - \frac{4}{x}=0,{\rm{  }}x > 0, type: solve(X – 4/X, X, 1) to get the solution x = 2.

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