Can someone help me with this assesment?
How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?

Your response must include:
•A summary of Descartes' rule and the Fundamental Theorem of Algebra. This must be in your own words.
•Two examples of the process ◦Provide two polynomials and predict the number of complex roots for each.
◦You must explain how you found the number of complex roots for each.

•At least 100 words in c

Question

Can someone help me with this assesment?
How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?
 
Your response must include:
 •A summary of Descartes' rule and the Fundamental Theorem of Algebra. This must be in your own words.
 •Two examples of the process ◦Provide two polynomials and predict the number of complex roots for each.
◦You must explain how you found the number of complex roots for each.
 
•At least 100 words in c

anonymous · Answer

Descartes' rule states that the possible number of the positive roots of a polynomial is equal to the number of sign changes in the coefficients of the terms or less than the sign changes by a multiple of 2.


Regardless if this is what you're looking for or not, it should assist you. I'm not going to do all the work for you, just gave you a general explanation.

The Fundamental Theorem of Algebra states that every polynomial equation over the field of complex numbers of degree higher than 1 has a complex solution, furthermore any polynomial of degree n has n roots. 
Remember that the complex numbers include the real numbers.


Suppose we are given the polynomial x^3+3x^2-x-x^4-2, we arrange the terms of the polynomial in the descending order of exponents:
-x^4+x^3+3x^2-x-2, count the number of sign changes, there are 2 sign changes in the polynomial, so the possible number of positive roots of the polynomial is 2 or 0.


returning to our polynomial above, -x^4+x^3+3x^2-x-2, it has degree 4 and so has n roots. Note that complex roots always come in pairs, so here is what can be said from these two rules: 
degree 1 has 1 real root
degree 2 has 2 real roots or 2 complex roots
degree 3 has 3 real roots or 1 real root and 2 complex roots
degree 4 has 4 real roots or 2 real roots and 2 complex roots 
note that if the degree is odd, there will be at least 1 real root

jdoe0001 · Answer

http://www.youtube.com/watch?v=5YAmwfT3Esc

anonymous · Answer

Thank you @skiller8860 ! And that's perfect! I didn't want the answer handed to me, just some help. Both of you were awesome! God bless you! Happy New Years!