The QUAD program on the TI-83

The QUAD program was developed in class to find numeric solutions to the general quadratic equation
ax²+bx+c=0 The listing of the program is:

To download, use the link QUAD.

Below are images showing the use of the program on the TI-83. We will be examining, in turn, the solutions to the equations x² + 6x + 8 = 0
x² + 6x + 9 = 0
x² + 6x + 10 = 0
x² + 6x + 7 = 0
8x² + 6x + 1 = 0

Figure 1 We start by pressing the key to obtain the menu of programs. Then we use the key to move the highlight down to the QUAD program, as shown in Figure 1.
Figure 2 We press the key to leave Figure 1 and produce the bottom line of the screen on Figure 2.

Figure 3 We press the key again to execute the QUAD program. Figure 3 shows the immediate result. The program asks for a value for the coefficient A. Since we are looking at the problem x² + 6x + 8 = 0 we know that the leading coefficient is 1. We have responded by pressing the key. This is the condition shown in Figure 3. Then we press to have the calculator accept our answer. This will move us to Figure 4.

Figure 4 The calculator requests the value of B. We respond with . The calculator asks for the value fo C. We press the key. This produces the image seen in Figure 4.

Figure 5 We leave Figure 4 by pressing the key. The calculator processes the information given and produces the result seen in Figure 5. In particular, we see that the value of the discriminant is 4, that there are two answers, and that those values are x=-2 and x=-4.

Figure 6 Next we want to run the program to solve x² + 6x + 9 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 6.

Figure 7 We leave Figure 6 by pressing the key. The calculator processes the information given and produces the result seen in Figure 7. In particular, we see that the value of the discriminant is 0, that there is one answers, and that answer is x=-3.

Figure 8 Next we want to run the program to solve x² + 6x + 10 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 8.

Figure 9 We leave Figure 8 by pressing the key. The calculator processes the information given and produces the result seen in Figure 9. In particular, we see that the value of the discriminant is -4, and that there are no Real Number answers.

Figure 10 Next we want to run the program to solve x² + 6x + 7 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 10.

Figure 11 We leave Figure 10 by pressing the key. The calculator processes the information given and produces the result seen in Figure 11. In particular, we see that the value of the discriminant is 8, that there are two answers, and that those values are x=-1.585786438 and x=-4.414213562. It is important to note that these are merely approximations to the correct answers. We note that the discriminant is 8, which is not a perfect square. Therefore, the answers will be irrational numbers. The calculator has provided an approximation to those irrational numbers. That is the best it can do given the programming that was done.

Figure 12 Finally, we want to run the program to solve 8x² + 6x + 1 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 12.

Figure 13 We leave Figure 12 by pressing the key. The calculator processes the information given and produces the result seen in Figure 13. In particular, we see that the value of the discriminant is 4, that there are two answers, and that those values are x=-1/4 and x=-1/2. In this case the calculator was able to express the answers exactly.

We noted in Figure 11 that when we have irrational answers, the QUAD program produces numeric approximations to those answers. A slightly enhanced version of the QUAD program is described in the quad1.htm page. That version produces the same values that are given by the QUAD program, but it also provides the more complete algebraic solution to the irrational answers.

Figure 1	We start by pressing the key to obtain the menu of programs. Then we use the key to move the highlight down to the QUAD program, as shown in Figure 1.
Figure 2	We press the key to leave Figure 1 and produce the bottom line of the screen on Figure 2.
Figure 3	We press the key again to execute the QUAD program. Figure 3 shows the immediate result. The program asks for a value for the coefficient A. Since we are looking at the problem x² + 6x + 8 = 0 we know that the leading coefficient is 1. We have responded by pressing the key. This is the condition shown in Figure 3. Then we press to have the calculator accept our answer. This will move us to Figure 4.
Figure 4	The calculator requests the value of B. We respond with . The calculator asks for the value fo C. We press the key. This produces the image seen in Figure 4.
Figure 5	We leave Figure 4 by pressing the key. The calculator processes the information given and produces the result seen in Figure 5. In particular, we see that the value of the discriminant is 4, that there are two answers, and that those values are x=-2 and x=-4.
Figure 6	Next we want to run the program to solve x² + 6x + 9 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 6.
Figure 7	We leave Figure 6 by pressing the key. The calculator processes the information given and produces the result seen in Figure 7. In particular, we see that the value of the discriminant is 0, that there is one answers, and that answer is x=-3.
Figure 8	Next we want to run the program to solve x² + 6x + 10 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 8.
Figure 9	We leave Figure 8 by pressing the key. The calculator processes the information given and produces the result seen in Figure 9. In particular, we see that the value of the discriminant is -4, and that there are no Real Number answers.
Figure 10	Next we want to run the program to solve x² + 6x + 7 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 10.
Figure 11	We leave Figure 10 by pressing the key. The calculator processes the information given and produces the result seen in Figure 11. In particular, we see that the value of the discriminant is 8, that there are two answers, and that those values are x=-1.585786438 and x=-4.414213562. It is important to note that these are merely approximations to the correct answers. We note that the discriminant is 8, which is not a perfect square. Therefore, the answers will be irrational numbers. The calculator has provided an approximation to those irrational numbers. That is the best it can do given the programming that was done.
Figure 12	Finally, we want to run the program to solve 8x² + 6x + 1 = 0 We can run the program again by pressing the key. Again the program requests the coeeficients, one at a time. We supply those values to leave the screen as shown in Figure 12.
Figure 13	We leave Figure 12 by pressing the key. The calculator processes the information given and produces the result seen in Figure 13. In particular, we see that the value of the discriminant is 4, that there are two answers, and that those values are x=-1/4 and x=-1/2. In this case the calculator was able to express the answers exactly.