Using the Theorem on Symmetric Functions or otherwise,

show that the discriminant of the quartic polynomial x^4 + qx + r

is 27q^4 + 256r^3.

Now, using the Symmetric Functions theorem, it's obvious that q= -s3 and r=s4 (where s3 and s4 are the third and fourth elementary symmetric polynomials). How do I proceed from here?

Many thanks.