Question: Can Maple find a determinant corresponding to a symbolic equation?

For exaqmple, the quadratic equation w^2 + uw + v = 0 corresponds to the deter minant


| -u  1  1  |

| v    0  1  |  = 0

|w^2 w w-1|

Is there any way to find a determinant corresponding to an equation, as above?

This is an issue in the preparation of a nomograph for the initial equation.  

It is generally solved by trial and error.

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