Have you heard of Sylvester's Condition?
So, in a nutshell, what it says is that you start looking at (top left) 1x1 2x2 3x3 ... nxn blocks of matrices all have positive determinants.
As a corollary, a matrix with negative determinant can never be positive definite.
In your example, no matter what x is, the determinant is always -1 which by Sylvester's Condition (Note : It is IFF) is not positive definite.
Now that you clarified in the comments what you mean by "get". It makes more sense.
Think about it, if the entire top row wasn't zero: Apply the Sylvester's Criterion.
The first 1x1 block is just 0 which is OK (but the matrix can't be positive definite, at most semidefinite)
The next block is 2x2 which has determinant $-x^2$. As long as you choose a real value of $x$, the criterion won't hold and you don't even need to go ahead if $x$ wasn't zero. However since we want a positive definite matrix, let's set $x=0$ and continue.
If you carry out the same determinant criterion on the entire matrix you'll realize that $y$ needs to be zero as well (Assuming $z\geq0$. Else the determinant will be negative. (The determinant is $-zy^2$)