Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - 5.7 Exercises - Skill Practice - Page 384: 34

Positive real root =1 Negative real root= 1 Imaginary roots: 2

In the given polynomial of degree $4$ , there are $4$ zeros. By Descartes' Rule, we have $1$ positive real root. $f(-x)=(-x)^4-(-x)^2-6=x^4-x^2-6$ The above polynomial shows that there is 1 sign change. By Descartes' Rule, we have $1$ negative real root. Thus, the other two roots must be imaginary. Positive real root =1 Negative real root= 1 Imaginary roots: 2