Question

What is the maximum number of non-real zeros possible for the function f? Give a reason for your answer.

a) 0
b) 1
c) 2
d) Infinite

Answer 1

Without the degree of the polynomial, we cannot accurately determine the maximum number of non-real zeros, but it cannot be infinite since every polynomial has a finite number of zeros.

Step-by-step explanation:

The maximum number of non-real zeros for a function depends on the degree of the polynomial. According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n roots, some of which may be non-real, and they always come in conjugate pairs. Therefore, if the degree of the polynomial is not given, it is impossible to determine the exact maximum number of non-real zeros. However, if we are to pick from the options provided and assume the students are studying polynomial functions, option (d) Infinite cannot be correct since any polynomial of degree n can have at most n roots, including real and non-real. Without more information, such as the degree of the polynomial, we cannot determine the maximum number of non-real zeros.