Three students were asked how they would verify their solution of a quadratic equation, $\left(x-2\right)\left(x-5\right)=0.$ Shown below are their responses.

Student $1$ said, "In the first bracket, $x$ must equal $2,$ and in the second bracket, $x$ must equal $5.$ So $\left(2-2\right)\left(5-5\right)=0.$"

Student $2$ said, "In the first bracket,$x$ must equal $2$, but in the second bracket, $x$ can have any real number value. For example $\left(2-2\right)\left(3-5\right)=0$ or $\left(2-2\right)\left(10-5\right)=0.$"

Student $3$ said, "Both brackets should always have the same $x$ value. So, $x$ is either $2$ or $5$ in both brackets. For example, $\left(2-2\right)\left(2-5\right)=0$ and $\left(5-2\right)\left(5-5\right)=0.$"

Whose response is correct$?$