Inconclusive Second derivative test ,Now how shall i proceed While doing maxima and minima questions i have encountered upon question in which i cannot show nature of points 
P1 : Given $f(x,y) = 2x^4 - 3x^{2}y + y^{2}$
Doubtful case is as origin .
P2: $f(x,y)$ = $y^{2} + x^{4} +x^{2}y $
Doubtful case is at origin
Thanks for help ..

P1: The function is $0$ on the curves $y = x^2$ and $y = 2 x^2$, is negative in between them and positive otherwise. So $(0,0)$ is a saddle point since there are positive and negative values of $f$ arbitrarily close to $(0,0)$. The fact that it is a saddle does not follow simply from the discriminant being $0$, for example the origin is a minimum for $g(x,y,)=x^4+y^4$.
