Determine the maximum number of real zeros that the following polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the polynomial function may have. Do not attempt to find the zeros.
What is the maximum number of zeros that
4 (Type a whole number.)
How many positive real zeros may the function
2,0 (Type a whole number. Use a comma to separate answers as needed.)
How many negative real zeros may the function
(Type a whole number. Use a comma to separate answers as needed.)
Final Answer: The maximum number of zeros that
Step 1 :The maximum number of real zeros a polynomial can have is equal to its degree. In this case, the degree of the polynomial is 4, so the maximum number of real zeros is 4.
Step 2 :Descartes' Rule of Signs states that the number of positive real zeros of a polynomial is equal to the number of sign changes in the polynomial's terms, or less than that by an even number. The polynomial
Step 3 :To find the number of negative real zeros, we substitute
Step 4 :Final Answer: The maximum number of zeros that