Let a ≠ b be two non-zero real numbers. Then the number of elements in the set X={z ∈ C: Re (a z^2+b z)=a. and. Re (b z^2+a z)=b} is equal to

Let $\displaystyle a \neq b$ be two non-zero real numbers. Then the number of elements in the set $\displaystyle X=\left\{z \in \mathbb{C}: \operatorname{Re}\left(a z^2+b z\right)=a\right.$ and $\displaystyle \left.\operatorname{Re}\left(b z^2+a z\right)=b\right\}$ is equal to