How the number of sign changes of a polynomial helps us determine the number or real zeros

The video tutorial explains the concept of real and imaginary solutions, focusing on positive and negative forms of equations. It guides students through simplifying negative forms and determining the number of real solutions using sign changes. The tutorial also covers analyzing zeros and the degree of polynomials, emphasizing the relationship between the degree and the number of zeros, which can be real or imaginary.

What are the two types of real solutions discussed in the video?

• Positive and imaginary

• Imaginary and complex

• Real and complex

• Real positive and real negative

When inserting negative X in a polynomial, what happens to a negative term raised to an even power?

• It remains negative

• It becomes positive

• It becomes zero

• It doubles

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

• By finding changes in signs from positive to negative

• By multiplying all terms

• By adding all coefficients

• By counting the number of terms

What rule helps determine the number of possible real and imaginary solutions?

• Euler's Formula

• Newton's Law

• Card's Rule of Signs

• Pythagorean Theorem

What is the degree of a polynomial with three zeros?

• Four

• One

• Two

• Three

If a polynomial has a degree of three, how many real negative solutions can it have?

• Zero or two

• One or three

• Two or four

• Three or five

What type of solutions can a polynomial have if it has one real negative solution?

• Two real positive solutions

• No other solutions

• Two imaginary solutions

• One real positive solution