Applying descartes rule of signs to determine the number or real positive & negative zeros

The video tutorial explains Descartes' Rule of Signs, which helps determine the number of positive, negative, and imaginary zeros in a polynomial equation. The instructor demonstrates how to evaluate the function for negative X and identify sign changes to find real zeros. The tutorial concludes with a summary of possible solutions based on the degree of the polynomial.

What does Descartes' Rule of Signs help determine in a polynomial equation?

• The roots of a quadratic equation

• The coefficients of the polynomial

• The number of positive, negative, and imaginary zeros

• The degree of the polynomial

When evaluating a polynomial for negative X, what is the first step?

• Multiply all coefficients by -1

• Replace X with negative X in the equation

• Add 1 to all exponents

• Divide the polynomial by X

What happens when a negative variable is raised to an even power?

• It remains negative

• It becomes zero

• It becomes positive

• It becomes undefined

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

• By evaluating the polynomial at zero

• By finding the degree of the polynomial

• By counting the number of terms

• By counting the number of sign changes

If a polynomial has a degree of 3, how many zeros should it have?

• One

• Three

• Four

• Two

What does it mean if there are zero positive real zeros in a polynomial?

• All zeros are positive

• All zeros are negative

• The polynomial has no zeros

• There must be imaginary zeros

What are the possible types of solutions indicated by Descartes' Rule of Signs?

• No solutions

• Both real and imaginary solutions

• Only imaginary solutions

• Only real solutions