how do I know which roots are repeated on the calculator?

[PG1995]

Hi

I was trying to find roots of some equations using the calculator TI-92 Plus (Voyage 200 and TI-89 are similar in functionality to 92 Plus). The calculator only gives me distinct roots and I can't know which roots are repeated. For an example, please have a look on the attachment. Thanks for the help.

Regards
PG

 

[MrAl]

Hi,

If it is already factored like that you can see that the m^3 term causes three zero solutions.

If not, you can divide by the known roots and reduce the equation to a lower order equation and go from there.
For example, since a root is -1 divide by (m+1) first, then for -2 divide by (m+2), etc.

There might be another trick out there too.

For example:
m^5+11*m^4+46*m^3+92*m^2+88*m+32=0

gives solutions -1, -2, and -4.

Dividing that by (m+1), it goes into it evenly with no remainder. Dividing by (m+1) a second time will show a remainder which means -1 is only a solution one time.
Dividing by (m+4) will do the same thing as (m+1) so -4 is a solution only once also.
If you did (m+2) before (m+4) however, you would find that (m+2) goes into that equation more than one time without causing a remainder. It would work a total of 3 times because -2 is a repeated root 3 times.

The only caution is when you're dealing with floating point numbers. This example worked out to all integers, but many solutions have floating point numbers which may cause a small remainder so you have to watch out for that. If the remainder is small be aware it may still be a repeated root. You can check by doing the math:
(m+1)*(m+2)*(m+2)*(m+2)*(m+4)
only with the floating point numbers, to see if it works out.

You might also run into this problem illustrated with this equation:
m^3+7.14159265*m^2+16.566371*m+12.566371=0

which gives solutions on the TI:
-1.99941, -2.00059, -3.14159

where we can see that the first two are almost the same, and the last one is almost equal to -pi. You have to judge whether or not the first two really are the same and represent a repeated root of say -2, while the last one is very close to -pi and may be the right solution if the original equation was given in more precision.

 

[ljcox]

I don't see why you need a calculator to solve this equation.

Obviously m1 = m2 = m3 = 0 and you solve the quadratic for m4 & m5.

Am I missing something?

Where would I find the calculator? Is it free software?

 

[MrAl]

Hi Len,

I assumed that he was asking a more general question about how to do this for any equation, not just the one given. I gave another example too which is harder to see the solutions to:
m^5+11*m^4+46*m^3+92*m^2+88*m+32=0

He probably doesnt want to have to factor it by hand either.

Actually there is a virtual TI that does what the TI can do that is available for download, but it requires a ROM file that can only be downloaded if you own the real life calculator already. You could check though just in case they released some version for people who dont have the calculator. All the stuff can be found on the TI site, or at least it used to be there several years ago.

Here's a screen shot:

 

[johnseal72]

Obviously m1 = m2 = m3 = 0 and you solve the quadratic for m4 & m5.

 

[MrAl]

john,

You missed the point...the point is not to do this single problem but to do ANY problem.

 

[ljcox]

Hi Len,

I assumed that he was asking a more general question about how to do this for any equation, not just the one given. I gave another example too which is harder to see the solutions to:
m^5+11*m^4+46*m^3+92*m^2+88*m+32=0

He probably doesnt want to have to factor it by hand either.

Actually there is a virtual TI that does what the TI can do that is available for download, but it requires a ROM file that can only be downloaded if you own the real life calculator already. You could check though just in case they released some version for people who dont have the calculator. All the stuff can be found on the TI site, or at least it used to be there several years ago.

Here's a screen shot:

Thanks Mr Al,
I wondered whether he was looking for a general solution rather than a specific one, but you never know with homework questions.

 

[PG1995]

Thanks a lot, MrAl.

I have found a solution. I was asking a general question to solve any equation. But I see I chose somewhat bad example equation.

Once again, thank you, MrAl.

Best wishes
PG

 

[MrAl]

Hi PG,


You're welcome, but i'd like to see the solution you found too. Did you find a more general and/or simpler solution?

 

[PG1995]

Hi MrAl

You need to use cFactor() function of the calculator (Factor() command also works but it won't help you with complex roots). cFactor() will easily let you see which roots are repeated. To me, it looks simple.

Best wishes
PG