The number of values of k for which the linear equations  4x+ky+2z=0, kx+4y+z=0, 2x+2y+z=0  possess a non-zero solution is

The condition for a homogeneous system of equations to have a non-zero solution is Δ=0⇒4k2k41221=0⇒4[2]−k[k−2]+2[2k−8]=0⇒8−k2+2k+4k−16=0⇒k2−6k+8=0 ⇒k=2,4