The values of ‘α’ for which the system of equations x+y+z=1,x+2y+4z=α,x+4y+10z=α2 is consistent are given by

x+y+z=1----(1)x+2y+4z=α-----(2)x+4y+10z=α2-----(3)(2)−(1)⇒ y+3z=α−1(3)−(1)⇒ 3y+9z=α2−1⇒3(α-1)=α2-1⇒α2-3α+2=0⇒(α-1)(α-2)=0α=1,2