How to apply Descartes rule of signs for polynomials

The video tutorial explains how to find zeros in polynomials, including rational, irrational, and complex zeros. It introduces Descartes' Rule of Signs to determine the number of real zeros by counting sign changes in the polynomial. The Fundamental Theorem of Algebra is discussed, emphasizing that the degree of a polynomial indicates the total number of zeros, which can be real or complex. The tutorial provides examples and calculations to illustrate these concepts, helping students understand the possible combinations of zeros in a polynomial.

What types of zeros can a polynomial have?

• Only irrational zeros

• Rational, irrational, and complex zeros

• Only complex zeros

• Only rational zeros

What does Descartes' Rule of Signs help determine?

• The degree of a polynomial

• The number of real zeros

• The sum of the coefficients

• The number of complex zeros

How do you determine the number of negative real zeros?

• By counting the number of terms in the polynomial

• By evaluating the polynomial at positive values

• By counting sign changes in the polynomial evaluated at negative values

• By using the quadratic formula

According to the Fundamental Theorem of Algebra, what does the degree of a polynomial indicate?

• The number of terms in the polynomial

• The number of zeros the polynomial can have

• The sum of the coefficients

• The number of complex zeros

If a polynomial has a degree of 5, how many total zeros must it have?

• 3

• 4

• 5

• 6

What is a possible combination of zeros for a polynomial of degree 5 with 2 positive real zeros?

• 1 positive, 2 negative, 2 complex

• 2 positive, 1 negative, 2 complex

• 3 positive, 1 negative, 1 complex

• 2 positive, 2 negative, 1 complex

If a polynomial has 0 positive real zeros and 1 negative real zero, how many complex zeros does it have?

• 4

• 3

• 2

• 1