Algebra-2

To find a quartic function with only real zeros at and , we can construct a function in the form , where has no real zeros.

 

Analysis of this function:

- The factors and give zeros and .

- The factor has no real zeros since implies , which has no real solutions.

 

So, the quartic function with only real zeros at and is .

 

Let's expand .

 

First, expand :

.

 

Now, multiply by :

.

 

Analysis of Options:

A. :

   - This is the function we obtained by expanding our constructed quartic function.

   - Conclusion: This function has zeros at and .

 

B. :

   - To check if

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