Question

find a differential operator that annihilates the given function.

$3x^2-6x+1$

Short answer

$D^3$is the differential operator that annihilates the given function.

Step-by-step solution

Differentiate the function continuously

Let the function be$f\left(x\right)=3x^2-6x+1$

Then

$$\begin{gathered} f\text{'}\left(x\right)=6x-6 \\ f\text{'}\text{'}\left(x\right)=6 \\ f\text{'}\text{'}\text{'}\left(x\right)=0 \end{gathered}$$

Hence$D^3\left[f\right]=0$

Then$D^3$ is the differential operator that annihilates the given function.