If the system of equations(a−t)x+by+cz=0bx+(c−t)y+az=0cx+ay+(b−t)z=0has non-trivial solution, then product of all possible values of t is

The given system of equations will have a non-trivial solution if the determinant of coefficients is 0.Δ=a−tbcbc−tacab−t=0              ………. (1)∆=0 is a cubic equation in t, so it has 3 solutions say t1, t2 and t3.Let Δ=p0t3+p1t2+p2t+p3,Clearly, po = coeff. of t3 which is equal to -1, sot1t2t3=−p3(−1)=p3= Constant term in the expansion of Δ i.e. Δ(t=0).Hence, t1t2t3=abcbcacab