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

f(x)=(2a−1)x2+2(a+1)x+(2a−1)x2−2x+40Since, 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                      (1)and D < 0⇒ 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