How to find the number of real and complex zeros using descartes rule of signs

The video tutorial explains how to determine the possible zeros of a polynomial using the rational zero test and Descartes' Rule of Signs. It covers the distinction between rational and irrational zeros, the process of finding negative real zeros, and the concept of symmetry in polynomials. The tutorial also discusses the fundamental theorem of algebra and explores different scenarios for the number of real and complex zeros.

What does the rational zero test help determine in a polynomial?

• The number of irrational zeros

• The possible rational zeros

• The degree of the polynomial

• The number of complex zeros

How can the number of sign changes in a polynomial help?

• It reveals the polynomial's symmetry

• It shows the number of complex zeros

• It indicates the number of real positive zeros

• It determines the polynomial's degree

What does substituting negative x into a polynomial help identify?

• The number of positive real zeros

• The polynomial's degree

• The number of negative real zeros

• The number of complex zeros

What does symmetry about the y-axis indicate when substituting negative x?

• The function is unchanged

• The function is complex

• The function is inverted

• The function is shifted

According to the fundamental theorem of algebra, what does the degree of a polynomial indicate?

• The total number of zeros

• The number of possible rational zeros

• The number of terms in the polynomial

• The number of sign changes

How many total zeros does a polynomial of degree 4 have?

• 2

• 3

• 4

• 5

What is the possible number of complex zeros if a polynomial has one real positive and one real negative zero?

• 1

• 2

• 0

• 3