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. :

   - To check if and are zeros, we can substitute these values into the function.

   - For : .

   - For