HP50g: How to display repeated roots and simplifying answers

[Fanboy]

Hi, I was using my 50g to solve for higher degree polynomials and I noticed that the 50G omits displaying roots which are repeated. Example: m^5 + 5m^4 -2m^3 -10m^2 +m +5 = 0
The calculator only gives 3 answers instead of all 5. Can I change this? It's important that I see all the roots. Mt Ti 84 already does this but it can't give exact answers which is why I'm using the 50g.

Also, I was wondering about the simplification functions built in to the 50g. I'm also using the 50g for solving integrals and I often get a huge mess of an answer (which can be simplified). The 'simplify' function doesn't really work in most cases for me. Can I simplify an expression with multiple natural logs or is this a limitation of the calculator?

[Joe Horn]

(09-26-2014 09:06 PM)Fanboy Wrote:  Hi, I was using my 50g to solve for higher degree polynomials and I noticed that the 50G omits displaying roots which are repeated. Example: m^5 + 5m^4 -2m^3 -10m^2 +m +5 = 0
The calculator only gives 3 answers instead of all 5. Can I change this? It's important that I see all the roots. Mt Ti 84 already does this but it can't give exact answers which is why I'm using the 50g.

When you execute SOLVE or SOLVEVX on a non-equation, it is automatically set equal to zero if it's not an equation, and it returns the "zeros" of the equation(aka roots, aka places where the curve crosses the X axis). When your polynomial is set equal to zero, then there ARE only 3 roots, 2 of which have a multiplicity of 2. If you execute FACTOR on your non-equation polynomial, you can see why; it's equal to this:

(m+5) * (m-1)^2 * (m+1)^2

In other words, if you set THAT equal to 0, the roots are obviously -5, -1, and 1. If you want to see the multiplicity of roots, use FACTOR or FACTORS instead of SOLVE or SOLVEVX.

The 50g has many ways to do things. Other ways of obtaining roots with multiplicities will probably be mentioned here by other folks.

(09-26-2014 09:06 PM)Fanboy Wrote:  Also, I was wondering about the simplification functions built in to the 50g. I'm also using the 50g for solving integrals and I often get a huge mess of an answer (which can be simplified). The 'simplify' function doesn't really work in most cases for me. Can I simplify an expression with multiple natural logs or is this a limitation of the calculator?

Be sure to try all the simplifications in the CONVERT / REWRITE menu (e.g. EXPLN, EXP2POW, LIN, LNCOLLECT, and POWEXPAND) as well the ALG menu (COLLECT, EXPAND, TEXPAND) and TSIMP. One or more of these will probably be what you need. I personally have found the sequence TSIMP EXP2POW so useful for simplification of messy things that I keep << TSIMP EXP2POW >> assigned to a key.

[Wes Loewer]

(09-26-2014 09:06 PM)Fanboy Wrote:  Hi, I was using my 50g to solve for higher degree polynomials and I noticed that the 50G omits displaying roots which are repeated. Example: m^5 + 5m^4 -2m^3 -10m^2 +m +5 = 0
The calculator only gives 3 answers instead of all 5. Can I change this? It's important that I see all the roots. Mt Ti 84 already does this but it can't give exact answers which is why I'm using the 50g.

As Joe pointed out, FACTORS is what you're looking for to give exact roots.

Just in case you were not aware of it, you can find the 5 roots numerically using PROOT. Unlike the 84+ PolySmlt2 APP, PROOT can accept complex coefficients.

-wes