Set of all real values of a such that f(x)=(2a−1)x2+2(a+1)x+(2a−1)x2−2x+40is always negative is

f(x)=(2a−1)x2+2(a+1)x+(2a−1)x2−2x+40 Since x2−2x+40>0 for all real x, (2a−1)x2+2(a+1)x+(2a−1)<0∀x∈R∴    2a−1<0 or a<12 and     D<0                                            (1)⇒    4(a+1)2−4(2a−1)2<0⇒    a(a−2)>0⇒    a<0 or a>2                                (2)From (1) and (2), a <0