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Setup:

R.<x> = PolynomialRing(ZZ)
A1 = R.random_element(degree=2)
C0 = R.random_element(degree=2)
C1 = R.random_element(degree=2)
S.<y> = PolynomialRing(R)

Execution:

sage: A1(y).resultant(C0 + y*C1)
x^4 - 6*x^3 + 5*x^2 - 4*x + 2