Applying Descartes rule of signs to identify the real and complex zeros

The video tutorial explains the rule of signs, which helps determine the number of real positive, real negative, and complex zeros in a polynomial. It covers how to find positive real zeros by counting sign changes and negative real zeros by substituting negative X. The tutorial also discusses complex zeros, emphasizing that they come in conjugate pairs and are always even in number. The degree of the polynomial determines the total number of zeros, which can be a combination of real and complex zeros.

What does the Rule of Signs help determine in a polynomial?

• The coefficients of the polynomial

• The number of real positive, real negative, and complex zeros

• The degree of the polynomial

• The number of terms in the polynomial

How do you find the number of positive real zeros in a polynomial?

• By finding the degree of the polynomial

• By substituting negative X

• By counting the sign changes between terms

• By counting the number of terms

What is the first step in finding negative real zeros?

• Add the coefficients

• Find the degree of the polynomial

• Substitute negative X into the polynomial

• Count the sign changes

What happens to a negative number raised to an even power?

• It becomes zero

• It becomes positive

• It becomes complex

• It remains negative

How many zeros does a polynomial of degree three have?

• Four

• Three

• Two

• One

What is true about complex zeros in a polynomial?

• They are always real

• They are always positive

• They always appear in pairs

• They always appear in odd numbers

If a polynomial has two real and one negative zero, how many complex zeros does it have?

• Zero

• Three

• One

• Two