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Mathcad doesn't agree with your second example!
Alan
Success!
Luc
The snippet doesn't claim that the expression below the determinant IS the determinant, but even if we normalize in the equation the coefficient of omega^4 to 1 we get a different equation.
So something is wrong in the snippet or the equation does not relate to the determinant above.
Just a fun a way to find the zeros without using the symbolics.
You can use the numeric "root" function or alternatively a solve block to do the job.