Answer :
The function [tex]f(x) = 3x^15 - 17x^8 + 11x^4 - 6x + 23[/tex] has at most 15 zeros.
Here, we have,
To determine the number of zeros that the function
[tex]f(x) = 3x^15 - 17x^8 + 11x^4 - 6x + 23[/tex] has,
we can use the Fundamental Theorem of Algebra.
According to the Fundamental Theorem of Algebra, a polynomial of degree n can have at most n distinct zeros.
In this case, the degree of the polynomial is 15, so we can conclude that the function has at most 15 zeros.
However, the Fundamental Theorem of Algebra does not provide information about the actual number of zeros or their nature (real or complex).
To determine the exact number of zeros or their characteristics, further analysis or techniques such as factoring, synthetic division, or the use of graphical methods may be required.
Therefore, based on the given information, we can only say that the function [tex]f(x) = 3x^15 - 17x^8 + 11x^4 - 6x + 23[/tex] has at most 15 zeros.
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