Using Descartes rule of signs to find possible zeros

The video tutorial explains how to find the zeros of a polynomial, focusing on real and complex zeros. It covers the process of identifying positive zeros by counting sign changes in the polynomial function and discusses the handling of zero terms. The tutorial also explains the subtraction of even numbers from the count of sign changes to determine the number of positive zeros. Additionally, it addresses the calculation of negative zeros and complex solutions, emphasizing the importance of understanding the degree of the polynomial to find the total number of solutions.

What is the first step in finding positive zeros of a polynomial?

• Factor the polynomial completely

• Find the number of sign changes in the polynomial

• Set the polynomial equal to zero

• Calculate the derivative of the polynomial

Why is it unnecessary to include a zero term in the polynomial when finding zeros?

• Zero is neither positive nor negative

• Zero terms complicate the calculations

• Zero terms are only needed for synthetic division

• Zero terms are always positive

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

• By adding the number of sign changes

• By multiplying the sign changes by two

• By subtracting an odd number from the sign changes

• By subtracting an even number from the sign changes

What happens if you subtract too many even numbers when calculating zeros?

• You find more zeros than exist

• You end up with a zero polynomial

• You get a negative number of zeros

• You get a complex number of zeros

What is the result of raising a negative number to an even power?

• A positive number

• Zero

• An imaginary number

• A negative number

How many complex zeros are there if a polynomial of degree 4 has two positive zeros and zero negative zeros?

• One

• Two

• Four

• Zero

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

• Zero

• Two

• One

• Four