The number of real values of ‘a’ for which the system & equations x+ay−z=0,2x−y+az=0,ax+y+2z=0 has a non-trivial solution is

The condition for a homogeneous system to have a non-trivial solution is Δ=0⇒0a−12+a−1a2+a12=0⇒2+a0a−11−1a112=0⇒2+a0-2+a−a2−a−11+1=0⇒2+a=0, −2a+a2−2=0⇒a2−2a−2=0⇒a=1∓3