Let x < 1, then value of x2+22x+112x+1x+21331 is

Applying R1→R1−R2 and R2→R2−R3 reduce the determinant tox2−2x+1x−102x−2x−10331=(x−1)3−2(x−1)2                                          =(x−1)2(x−1−2)                                          =(x−1)2(x−3),which is clearly negative for x < 1.