"A monic quadratic is a quadratic in which the coefficient of the quadratic term is 1. For example, $r^2 - 3r + 7$ is a monic quadratic, but $3t^2 - 3t + 1$ is not.
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 quadratic and linear terms). 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 quadratic and constant terms). 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 quadratic that the teacher wrote on the board?"
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