The simplest Laguerre polynomials are $$ L_k(x)=(\frac{d}{dx}-1)^k\left(\frac{x^k}{k!}\right). $$ I would like to find a simple reference for proving or disproving the following assertions.

(1) All the $k$ zeroes of $L_k$ are simple and located on the positive half-line.

(2) The largest zero of $L_k$ is bounded above by $k^2$.