Re: Haw to find symbolick roots

"Kiril " <kkirqkov@xxxxxxxxx> wrote in message <gq7tnq$3lo$1@xxxxxxxxxxxxxxxxxx>...
Thanks for help ... may be u understand that I'm new here ( i asking stupid questions) but i want to as u only one thing : If I sub: x=f^2 so that
P= x^4 +a1*x^3 + a2*x^2 + a3*x + a4;
Is this equal to
P=0*f^8 + 0*f^7 + a1*f^6 + 0*f^5 + a2*f^4 + 0*f^3 + a3*f^2+ 0*f^1 + a4;
And if it is, is there are way to plot my roots ?

Kiril, you appear to have a typing error in

"P=0*f^8+0*f^7+a1*f^6+0*f^5+a2*f^4+0*f^3+a3*f^2+0*f^1+a4"

Based on your later remarks, it should be:

P=1*f^8+0*f^7+a1*f^6+0*f^5+a2*f^4+0*f^3+a3*f^2+0*f^1+a4

with a '1' coefficient in the 'f^8' term.

If so, you have an eighth degree polynomial equation for which in the general case there would be no symbolic solution. However, as John has pointed out, in your particular case it can be reduced to finding the roots of a quartic (fourth degree) polynomial equation using the substitution x = f^2. Quartics do have symbolic solutions. My own version of the Symbolic Toolbox is not smart enough to give it. Perhaps yours is. If not, many elementary algebra text books will have it.

When you convert back to roots of f there will be eight roots, because each root for x has two possible square roots for f, and therefore these can also be expressed symbolically.

As to your question about plotting the roots, what is it you are varying to produce a plot?

Also note that to do a plot, it is not necessary to have symbolic expressions for your roots. They can be obtained numerically using the matlab 'roots' function. Requiring explicit symbolic formulas for complicated functional relationships is sometimes a difficult or impossible task.

And finally, some of your eight roots may be complex-valued. Plotting these would be rather awkward to do.

Roger Stafford
.

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