1. The problem statement, all variables and given/known data ax^2 + 2bxy + cy^2 such that x,y are variables and a,b,c are scalars. Show that ax^2 + 2bxy + cy^2 ≥ 0 and =0 iff x,y=0 and iff b^2 - ac < 0 and a > 0 2. Relevant equations 3. The attempt at a solution This is actually a differential geometry problem, but I have it worked out all the way to this point. I'm proving the 4th axiom of inner products for this particular inner product and I just cannot find a factorization to help prove this inequality. If any of this doesn't make sense, just say so and I may be able to clarify.