If a2+b2+c2+2=0 and f(x)=1+a2x1+b2x1+c2x1+a2x1+b2x1+c2x1+a2x1+b2x1+c2x then f(x) is a polynomial of degree
0
1
2
3
Operating C1→C1+C2+C3, we get
f(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)2
which is a polynomial of degree 2.