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------------------------------------------------ How many real zeros do you expect for the function [tex]f(x) = 35x^{17} - 200x^{14} + 189x^{9} - 10x^{5} + 71x^{2} - 16x + 2000[/tex]?

A) 0 real zeros
B) 2 real zeros
C) 4 real zeros
D) 6 real zeros

To determine the number of real zeros, consider the degree of the polynomial function. The degree of the highest term, 35x^17, is 17. According to the Fundamental Theorem of Algebra, a polynomial of degree n can have up to n real zeros. Therefore, in this case, the function can have up to 17 real zeros.

However, the function may have repeated roots, and complex roots are also counted. The specific coefficients and structure of the polynomial will determine the exact number of real zeros. In this context, the given options indicate that the function is expected to have 6 real zeros.

Option D is the answer.

Learn more about Polynomial Zeros here:

https://brainly.com/question/28560646

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