Can you find the maximum number of possible real positive zeros, real negative zeros, and imaginary zeros of the function f(x) = x^6+4x^5-11x^4-12x^3+3x^2-2x+52?

Answer 1

Descartes rule of signs tells you that there is a maximum of 4 real positive roots and 1 real negative root.

Graphing the equation suggests that there are 3 real roots!

All my learning says this is NOT possible since complex conjugate roots must occur in pairs.

I do not understand this and will have to study it further.

If you get a better answer either here or in class, I would appreciate your letting me know.

Thanks!

4/30/2019

I am sorry this took so long and it may be no longer of any help to you.

The equation has 4 real roots (not 3) and 2 were so close together I could not see them on my graphing calculator. Therefore: 4 real roots and one pair of complex conjugates!