The main theorem of this article states that there are no nodal algebras \(A\) satisfying: (I) \(x(xy) (yx)x = 2(xy)x,\) (II) \((xy)x - x(yx)\) is nilpotent for any element \(x\) and \(y\) in \(A\) over any field \(F\) of characteristic zero. The result of Gerstenhaber that if \(x\) is a nilpotent element of a commutative power-associative algebra over a field of characteristic zero then \(R_x\) is a nilpotent operator, is frequently used in the proof. The author also provides several results regarding algebras satisfying only condition (I). In particular if \(A\) is any algebra satisfying (I) and \(A^+\) is power-associative then \(A\) is also power-associative.