Algebra-2

To find a quartic function with only real zeros at x = 9 and x = -1, we can construct the function based on the given roots. The function must include these zeros in such a way that the total degree is 4 and there are no additional real zeros.

 

Analysis of Options:

A. :

   - Real Zeros: The zeros from (x - 9), (x + 1), and are x = 9, x = -1, and x = 1.

   - Total Zeros: This function has three real zeros instead of only two required zeros.

   - Conclusion: This function does not meet the requirement.

 

B. :

   - Real Zeros: The zeros from (x - 9) and (x + 1) are x = 9 and x = -1. The factor () has complex zeros x = i and x = -i.

   - Conclusion: This function has only the real zeros x = 9 and x = -1, so it meets the requirement.

 

C.

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