If f(x) | array ccc 1 & x & x+1 2 x & x(x-1) & x(x+1) 3 x(x-1) & x(x-1)(x-2) & (x-1) x(x+1) array | then f(2012) is equal to

Step-by-step solution

Given, f(x)= | array ccc 1 & x & x+1 2 x & x(x-1) & x(x+1) 3 x(x-1) & x(x-1)(x-2) & (x-1)(x)(x+1) array | Taking x and x(x-1) common from R₂ and R₃ and (x+1) common from C₃=x x(x-1) (x+1) | array ccc 1 & x & 1 2 & (x-1) & 1 3 & (x-2) & 1 array | (applying C₂ C₁+C₂ ) aligned & =x^2 (x^2-1 ) | array lll 1 & x+1 & 1 2 & x+1 & 1 3 & x+1 & 1 array | & =x^2 (x^2-1 )(x+1) | array lll 1 & 1 & 1 2 & 1 & 1 3 & 1 & 1 array |=0 & f(x)=0 & f(2012)=0 aligned