Consider the matrix A=(1xx21yy21zz2)A = \begin{pmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{pmatrix}A=111xyzx2y2z2. For which of the following is det(A)=0\det(A) = 0det(A)=0?
x=yx=yx=y
x=zx=zx=z
y=zy=zy=z
x+y+z=0x+y+z=0x+y+z=0