how to find root of of a polynomial whose higest order is more than 3

[samina]

for drawing root locus i need to know how to find root of a polynomial whose highest order would be more than 4,
i need to know a short cut method as it is only a small part of the whole math( need it for finding break away point of root locus)
please please help

 

[BrownOut]

Been a long time, but try looking up synthetic division.

 

[samina]

thanks so much for ur quick reply
synthetic division- whats that? can u tell me something

 

[BrownOut]

Just look it up. I'm sure there is alot of information on the web. Don't make me go back 25 years and try to remember...

 

[The Electrician]

Here is an applet that will find the roots of a polynomial up to 5th degree:

https://www.elmer.unibas.ch/pendulum/polyroot.htm

Mathematical programs that are usually available at universities, such as Mathematica, Maple, Matlab, Derive, Scilab, etc., can usually solve high degree polynomials.

Also, newer scientific calculators such as the TI86, TI89, HP48GX, HP49G+ and HP50G can find roots of polynomials to fairly high degree.

 

[Electronworks]

I seem to remember being taught that there was no formula for solving the roots of a polynomial greater than order 3. We were told to do it using iterative methods: plug in a value, see what the result is, plug in a different value, see what the result is... ad nausium...

But then I did this last when Hollywood was black and white and the actors used to walk fast...

 

[Mikebits]

You need to find your p and q values for real zeros and then test each one. Quite tedious.
Rational Zeros of Polynomials

 

[MrAl]

Hi there,


Believe it or not, there is an analytical solution to a fourth degree polynomial, but that solution isnt that simple anyway. It would take a few lines of text here to display a solution for just *one* of the four roots.

For any degree, check out Lin-Bairstow or even just Bairstow on Wikipedia which has a worked out example using Bairstow's Method and some good links too.

You should also keep in mind that regular floating point may not work for degrees above 8 or so. One way to test is to evaluate the polynomial to see if it really reaches a true zero with the supposed solution found.

 

[The Electrician]

Believe it or not, there is an analytical solution to a fourth degree polynomial, but that solution isnt that simple anyway. It would take a few lines of text here to display a solution for just *one* of the four roots.

There's an analytical solution to the fifth degree as well:

"The general quintic can be solved in terms of Jacobi theta functions, as was first done by Hermite in 1858.

http://mathworld.wolfram.com/QuinticEquation.html"

if we admit Jacobian theta functions to our arsenal of functions that can be used to express a solution in closed form.

 

[mel8030]

Maybe write a small program using Newton's method.