If a^2+b^2+c^2=-2 and f(x)= | array ccc 1+a^2 x & (1+b^2 ) x & (1+c^2 ) x (1+a^2 ) x & 1+b^2 x & (1+c^2 ) x (1+a^2 ) x & (1+b^2 ) x & 1+c^2 x array | then f(x) is a polynomial of degree

Step-by-step solution

aligned & f(x)= | array ccc 1+ (a^2+b^2+c^2+2 ) x & (1+b^2 ) x & (1+c^2 ) x 1+ (a^2+b^2+c^2+2 ) x & 1+b^2 x & (1+c^2 ) x 1+ (a^2+b^2+c^2+2 ) x & (1+b^2 ) x & 1+c^2 x array | , Applying C₁ C₁+C₂+C₃ & = | array ccc 1 & (1+b^2 ) x & (1+c^2 ) x 1 & 1+b^2 x & (1+c^2 ) x 1 & (1+b^2 ) x & 1+c^2 x array | a^2+b^2+c^2+2=0 & f(x)= | array ccc 0 & x-1 & 0 0 & 1-x & x-1 1 & (1+b^2 ) x & 1+c x array | ; Applying R₁ R₁-R₂, R₂ R₂-R₃ & f(x)=(x-1)^2 aligned Hence degree =2 .