Spring $k_1$ is compressed, and $k_2$ expanded by distance x
Using conservation of energy
the total potential energy of the spring= Kinetic energy of the mass
$\large\frac{1}{2}$$k_2x^2+\large\frac{1}{2}$$k_1x^2=\large\frac{1}{2}$$mv^2$
$v=x \sqrt {\large\frac{k_1+k_2}{m}}$
Hence cis the correct answer.