Algebra-2

To find a quartic function with only real zeros at x = 3 and x = -6, 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 - 3) and (x + 6) are x = 3 and x = -6. The factor gives zeros x = -1 (with multiplicity 2).

Total Zeros: This function has zeros at x = 3, x = -6, and x = -1, which are not the required zeros.

Conclusion: This function does not meet the requirement.

 

B.

Real Zeros: The zeros from (x + 3) and (x - 6) are x = -3 and x = 6.

Total Zeros: This function has zeros at x = -3 and x = 6, which are not the required zeros.

Conclusion: This function does not meet the requirement.

 

C.

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