QQ[a, b, c, x]
((a-b))^2 + discriminant((x-a)*(x-b),x)
((a-b)*(a-c)*(b-c))^2 + discriminant((x-a)*(x-b)*(x-c),x)
discriminant(x^2+b*x+c, x)

end
--    Is the sign right?

i10 : QQ[a, b, c, x]

o10 = QQ[a, b, c, x]

o10 : PolynomialRing

i11 : ((a-b))^2 + discriminant((x-a)*(x-b),x)

o11 = 0

o11 : QQ[a, b, c, x]

i12 : ((a-b)*(a-c)*(b-c))^2 + discriminant((x-a)*(x-b)*(x-c),x)

o12 = 0

o12 : QQ[a, b, c, x]

i22 : discriminant(x^2+b*x+c, x)

         2
o22 = - b  + 4c

o22 : QQ[a, b, c, x]
