how you could use Descartes' rule and the Fundamental Theorem to predict the number of complex roots to a poly

Question

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.

Answer 1

Since it's not explicitly stated, I think it might be helpful to add that all Real numbers are also Complex numbers.   (If you had a Venn diagram of real numbers and complex numbers,  the Real Numbers would be a circle inside the Complex Numbers).

Answer 2

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