Quote Originally Posted by HallsofIvy View Post
No, it's not. "0= 0" is true for any values of A and B.

If both A and B satisfy x^2+ Ax+ B= 0 then A^2+ A(A)+ B= 2A^2+ B= 0, so that B= -A^2, and B^2+ AB+ B= 0. Since B= -A^2, (-A^2)^2+ A(-A^2)+ (-A^2)= A^4- A^3- A^2= A^2(A^2- A- 1)= 0.