1. ## annihilators

Can someone help me with this one?
Find the operator that annihilates this function
x^4 - x^2 + 11

I wanna say that the solution is:
for x^4 L1 = D^5 and for x^2 L2 = D^3
So L1L2 = D^8
but this is the wrong answer and I am confused. Thanks.

2. Originally Posted by pberardi
Can someone help me with this one?
Find the operator that annihilates this function
x^4 - x^2 + 11

I wanna say that the solution is:
for x^4 L1 = D^5 and for x^2 L2 = D^3
So L1L2 = D^8
but this is the wrong answer and I am confused. Thanks.
There's lots of operators that will annilate this but the easiest is $D^5$ noting that this operator will annilate everything up to $x^4$ which includes $x^2\;\text{and}\; 11.$

3. I see but D^5 is the minimum annihilator right? Thanks.