Let a , x , y , z be real numbers satisfying the equations a x + a y = z x + a y = z x + a y = a z , where x , y , z are not all zero, then the number of the possible values of a is

Step-by-step solution

As x , y , z are not all zero, thus the system has a non-trivial solution. Thus, D = 0 ⇒ a a - 1 1 a - 1 1 a - a = 0 ⇒ a a 2 - a - a a - 1 + 1 a - a = 0 or a 3 - a 2 - a 2 + a = 0 ⇒ a a 2 - 2 a + 1 = 0 ⇒ a = 0 , 1