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(if a,b,c,d are known) what is a clever method to solving for the value k if we are given the following:

the above polynomial is equal to the following(zeta is given as some constant, say 1 for simplicity):

(s+alpha)(s+beta)(s+gamma)(s+lamda)(s^2+2w*zeta*s+w^2)

we would have to multiply out this expression that seperate out coefficients for s and equation to a,b,c, and d

we then have a system of 6 nonlinear equations to solve for 6 unknowns

what is the fastest way to do this by hand within a 20 minute timeframe?