A teacher writes a monic quadratic on the board. Joanie copies the quadratic onto her paper, but writes down the wrong constant term (but the correct linear term). She correctly factors the quadratic that she wrote down on her paper, and determines that her quadratic has roots $-16$ and $2.$ Kelvin is factoring the same quadratic that the teacher wrote on the board. He also copies the quadratic onto his paper, but he writes down the wrong coefficient for the linear term (but the correct constant term). He correctly factors the quadratic that he wrote down, and determines that his quadratic has roots $-36$ and $2.$ What are the roots of the actual quadratic that the teacher wrote on the board?