Let $V$ be the vector space of real polynomials with degree less than 4. Let $W$ be the subspace of polynomials with degree less than 2. Consider the linear operator $L:V\to V$ defined by $L(p(x)):=-6 p'(x)+1 p(x)$. It is easy to see that $W$ is invariant under $L$. Define the linear operator $K$ on the quotient space $V/W$ by $K(p(x)+W):= L(p(x))+W$. Find the characteristic polynomial $f(t)$ of $K$.
$f(t) =$