# HP 48G equation solver and multiple solutions

• Calc Curious
In summary: Thanks for your input!I own a Ti 89 and it can solve polynomials for all its solutions, without any guesswork, as long as it's in an 'unrearranged form'.
Calc Curious
Dear all,

I am currently completing a water engineering subject at university as part of my civil engineering studies. For this subject (and probably others in future), I occasionally need to solve for an unknown value in a quadratic or cubic function, where there are three possible solutions and I need to know all three (to do with depths in open channel flows, one is negative so we discard it, one is for subcritical flow, and the other is for supercritical flow).

I own three HP calculators, the 42S, the 11C and the 48G (having heard only good things about them), and only the 48G has an algrebraic equation solver which would be useful in such a scenario. I thought the 48G would be able to solve these problems in an instant, but instead I find when using the equation solver that it never gives me more than one answer, even for a quadratic (no matter how many times I press 'solve'). I tried looking in the user guide but couldn't see anything that offered any clues.

Am I simply doing something wrong, or does the equation solver on this machine only give one answer? I can't believe it couldn't handle something so basic.

If it's a calculator and not an operator problem, could someone please recommend me a calculator that can handle these sorts of problems quickly, for use in my final exam in June. We are allowed to use graphics calculators in our exams, even programmable ones, but programming isn't necessary for me. It wouldn't have to be HP (or RPN, but I do prefer that), a Ti would be fine, just anything quick and efficient that works.

Have you tried to solve a polynomial with known, distinct roots with your calculator?

According to the HP-48 Quick Start Guide, after entering the coefficients, you press SOLVE once and all the roots are stored in the stack. You have to scroll thru the stack to examine each root.

I had a look into the polynomial solver and yes it does appear to solve these sorts of problems, but it appears I would need to rearrange the equation into a form that fits into the matrix writer for it to work, which would be a concern in an exam scenario where time is precious. I'd be looking to manipulate the equation as little as possible, ideally, just punch it in and bang there are the results.

All you have to do is remember to enter the coefficients starting with the highest power of x.

I see, although there would still be some equation rearranging needing to take place for that to happen from the energy equations I'm dealing with. I've had a few practices and sometimes my algebra isn't foolproof and I'm still a bit concerned that in the exam there will be those with more up to date technology out there who will be able to get through the exam quicker and make fewer mistakes. I do struggle with time in exams. So now I know my 48G will handle these problems as long as I do all the equation rearranging myself, but if there are easier options out there on the market I will certainly consider them. Thanks again.

Had to do my own research on this one, to my knowledge the only calculators on the market which will solve a polynomial for all its solutions (without guesswork) where its in an 'unrearranged form' if anyone reading is wondering, is the Ti Nspire and the Ti 89 (preferably titanium). To my knowledge none of the HPs do, as they probably assume their users are magicians when it comes to algebra, other than that I'm sure they're great machines.

## 1. How do I use the equation solver on my HP 48G calculator?

To use the equation solver on your HP 48G calculator, follow these steps:
1. Press the EQN button on the calculator.
2. Enter the equation in the format "equation=0" (e.g. x^2-4=0).
3. Press the SOLVE button.
4. Use the arrow keys to select the variable you want to solve for.
5. Press ENTER to solve for the variable. If there are multiple solutions, press the up or down arrow keys to view them.
6. Press ENTER again to see the numerical value of the solution.

## 2. Can the HP 48G equation solver find multiple solutions?

Yes, the HP 48G equation solver can find multiple solutions to an equation. After pressing the SOLVE button, use the arrow keys to navigate through the solutions. Press ENTER to see the numerical value of each solution.

## 3. How accurate are the solutions provided by the HP 48G equation solver?

The accuracy of the solutions provided by the HP 48G equation solver depends on the accuracy of the input equation. The calculator uses a numerical method to approximate the solutions, so the accuracy may vary for different equations. It is always recommended to double-check the solutions provided by the calculator.

## 4. Can I use the equation solver to solve for multiple variables simultaneously?

No, the HP 48G equation solver can only solve for one variable at a time. If you have multiple variables in your equation, you will need to rearrange the equation and solve for one variable first, then substitute the solution into the equation to solve for the other variables.

## 5. Is the HP 48G equation solver capable of solving complex equations?

Yes, the HP 48G equation solver can handle complex equations, including equations with imaginary solutions. However, it is important to note that the calculator only provides numerical solutions and cannot show the complex roots in their exact form.

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