Use Descartes Rule of signs to determine the number of positive and negative

The video tutorial explains Descartes' Rule of Signs, which helps determine the number of positive and negative real zeros in a polynomial. The instructor demonstrates how to analyze sign variations in a polynomial to find possible positive and negative real zeros. By evaluating the polynomial with negative inputs, the instructor shows how to determine the number of negative real zeros. The tutorial concludes with a summary of the findings and encourages viewers to engage with the content.

What is the primary purpose of Descartes' Rule of Signs?

• To find the exact value of real zeros

• To determine the number of positive and negative real zeros

• To identify the coefficients of a polynomial

• To calculate the degree of a polynomial

How many sign variations are there in the polynomial H(x) = 4x^3 - 3x^2 + 2x - 1?

• 1

• 2

• 3

• 4

According to Descartes' Rule of Signs, what are the possible numbers of positive real zeros for the polynomial H(x) = 4x^3 - 3x^2 + 2x - 1?

• 3 or 1

• 1 or 0

• 2 or 0

• 4 or 2

What happens to the sign of a term when a negative x is raised to an odd power?

• It doubles

• It becomes positive

• It remains negative

• It becomes zero

What conclusion can be drawn if there are no sign variations when evaluating H(-x)?

• There are no negative real zeros

• There is one negative real zero

• All zeros are imaginary

• There are three negative real zeros