I am using a TI-83 calculator to find all the solutions to the quadratic equation (5x(Squared) - 80 = 0)by graphing. The answer is supposed to be (-4 and 4) but the calculator comes up with (ERR: NO SIGN CHNG). Can you tell me what I'm doing wrong?

Some numerical graphing/solving algorithms require the limits have different signs so that by marching through the interval, it is bound to find a root.

I do not know what Ti-83 uses, and do not know which macro you used to graph the equation. Try graphing from -5 to 0 and from 0 to 5, each should come up with a root of x=-4 and 4 respectively.

This problem applies to a numerical solution of general polynomial or other functions. If Ti-83 has a special function for quadratic equations, it should not have this problem.

Sure! The error message "ERR: NO SIGN CHNG" indicates that the graphing calculator cannot determine the solutions to the equation because there is no change in sign on the graph. This means that the quadratic equation you entered does not intersect the x-axis, meaning it has no real solutions.

Let's go through the steps to find the correct solutions to the quadratic equation (5x^2 - 80 = 0) using the TI-83 calculator:

1. Turn on your calculator and press the "MODE" button. Make sure you are in "Function" mode (Func), which is usually the first option.

2. Press the "Y=" button to enter the equation editor. Clear any existing equations by pressing the "Clear" button if necessary.

3. Enter the quadratic equation: 5x^2 - 80. You do not need to include "=0" because the calculator assumes the equation equals zero.

4. Press the "GRAPH" button to plot the graph of the equation.

5. Inspect the graph to see if it intersects or touches the x-axis. If you see that the graph does not cross or touch the x-axis, it means that the equation has no real solutions, which is consistent with the "ERR: NO SIGN CHNG" error message you received.

In this case, your quadratic equation (5x^2 - 80) does not have any real solutions. It represents a parabola that opens upward and does not intersect the x-axis.

Therefore, the correct answer is that the equation has no solutions, rather than (-4 and 4) as you mentioned.