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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
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.
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...
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.
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.
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