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Let f(x) denotes the determinant f(x) ...

Let f(x) denotes the determinant
f(x) = `|{:(x^(2),2x,1+x^(2)),(x^(2)+1,x+1,1),(x,-1,x-1):}|`
On expansion g(x) is seen to be a 4th degree polynomial given by f(X) =`a_(0)x^(4)+a_(1)x^(3)+a_(2)x^(2)+a_(3)x+a_(4)`.
Using differentiation of determinant or otherwise match the entries in Column I with one or more entries of the elements of Column II.

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