Algebra-2

To find a quartic function with only real zeros at x = 1 and x = -7, 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 - 1) and (x + 7) are x = 1 and x = -7.

Complex Zeros: The factor () has complex zeros x = i and x = -i.

Conclusion: This function has only the real zeros x = 1 and x = -7, so it meets the requirement.

 

B.

Real Zeros: The zeros from (x + 1) are x = -1 (with multiplicity 3) and x - 7 gives x = 7.

Total Zeros: This function has zeros at x = -1 and x = 7, which are not the required zeros.

Conclusion: This function does not meet the requirement.

 

C.

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