Can you find the maximum number of possible real positive zeros, real negative zeros, and imaginary zeros of the function f(x) = x^6+9x^5-11x^4-23x^3+2x^2-4x+3?

Answer 1

Descartes rule of signs tells you that the maximum # of real positive roots is 4 and real negative roots is 1.

The only easy way that I know of to answer the question about complex roots is to graph the equation. Every time that the function has a maximum or minimum without a zero crossing indicates a complex root pair.