How do i find sets of values

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Is this a Sage question? Please edit to rewrite this so it's clear what you want Sage to do.

Just an allusion:

sage: R.<k,x> = QQ[]
sage: f = k*x^2 + 4*x + k
sage: f.discriminant(x)
-4*k^2 + 16

Or:

sage: R.<k> = QQ[]
sage: Q = QuadraticForm( R, 2, [k/2,2,k/2] )
sage: Q.matrix()
[k 2]
[2 k]
sage: Q.disc()
-k^2 + 4