Consider the inner product $\langle p(x),q(x)\rangle:=\int_0^1 p(x)q(x) dx$ on the vector space $V$ of real polynomials with degree less than 2. The linear operator $L:V \to V$ is defined by $L(p(x))=-5 p'(x)+1 p(x)$. Find the adjoint $L^*$ of $L$.
$L^*(a+bx) =$ + $x$