HP 48G equation solver and multiple solutions

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Discussion Overview

The discussion centers around the capabilities of the HP 48G calculator in solving polynomial equations, particularly quadratic and cubic functions, within the context of civil engineering applications related to open channel flows. Participants explore the limitations of the calculator's equation solver and seek alternatives that can efficiently handle multiple solutions during exams.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses frustration that the HP 48G's equation solver only provides one solution for polynomial equations, questioning if this is a limitation of the calculator or user error.
  • Another participant suggests that the HP-48 can indeed solve polynomials with distinct roots, indicating that all roots are stored in the stack after pressing SOLVE, and that users need to scroll through the stack to view them.
  • A participant acknowledges the polynomial solver's capability but raises concerns about needing to rearrange equations into a specific form, which may be time-consuming during exams.
  • It is noted that entering coefficients in the correct order (starting with the highest power) is essential for the calculator to function properly.
  • One participant expresses anxiety about their algebra skills and the potential for other students with more advanced calculators to perform better in exams.
  • A later reply mentions that the TI Nspire and TI 89 calculators can solve polynomials for all solutions without requiring rearrangement, contrasting this with the HP calculators, which are perceived as less user-friendly in this regard.

Areas of Agreement / Disagreement

Participants generally agree that the HP 48G has limitations in solving polynomials without rearrangement, while there are competing views on the effectiveness of the calculator's features and the availability of alternative calculators that may better meet their needs.

Contextual Notes

Participants express concerns about the time required for rearranging equations and the potential for mistakes in algebra during exams, highlighting the need for calculators that can handle equations in their original forms efficiently.

Calc Curious
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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.
 
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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.
 
Thanks for your quick response.

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.
 

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