I've been doing some homework and I really don't understand a few things.
Can anyone explain to me how the Descartes' Rule and Fundamental theorem can be used to determine the number of complex roots (in a polynomial)?
Examples would be absolutely stellar!
Also, does anyone know what setting a "good window" (on a graphing calculator) is?
and what features of a polynomial should be given?
Thank you! :]
the stated there is the maximum number ONLY of positive real roots and not necessarily the number of positive real roots. (and respectively..)
why maximum and not the exact? if it is , the polynomial may possibly have complex roots.. (complex roots always come in pairs.)
counter-example: here, we have and .. our .. thus ?
however, for which there are 2 positive real roots, no negative real roots and 2 imaginary number roots.. thus, the equation is not necessarily true..