If a2+b2+c2=−2 and f(x)=1+a2x1+b2x1+c2x1+a2x1+b2x1+c2x1+a2x1+b2x1+c2x then f(x) is a polynomial of degree

Operating C1→C1+C2+C3, we getf(x)=1+2x+a2+b2+c2x1+b2x1+c2x1+2x+a2+b2+c2x1+b2x1+c2x1+2x+a2+b2+c2x1+b2x1+c2x     =11+b2x1+c2x11+b2x1+c2x11+b2x1+c2x ∵a2+b2+c2=−2     =11+b2x1+c2x01−x0001−x  [Operating R2→R2−R1 and R3→R3−R1    =(1)(1−x)2−0=(1−x)2which is a polynomial of degree 2.