Is a negative value on the Kelvin scale possible? Why?

(NO) No,a negative value on the Kelvin scale is not possible.
According to the kinetic theory of gases,the temperature of a system is directly proportional to the average kinetic energy of its molecules.
The absolute zero temperature $(0 \ K)$ corresponds to the state where the kinetic energy of the molecules becomes zero,meaning all molecular motion ceases.
Since kinetic energy cannot be negative,the temperature on the Kelvin scale cannot be less than $0 \ K$.