If x2 + 2(a - 1)x + a + 5 =0 has real roots belonging to the interval (1, 3) then aϵ
(−87, −1)
x2 + 2 (a - 1)x + a + 5 = 0 has roots ϵ (1, 3)
∴ Δ≥0, f(1)>0, f(3)>0, 1<−B2A<3⇒ 4(a−1)2−4(a+5)≥0 ⇒(1+a)(a−4)≥0⇒aϵ(−∞, −1]∪[4, ∞) ...(i)1+2(a−1)+a+5>0 ⇒ a>−43 ...(ii)9+2(9−1)3+a+5>0 ⇒a>−87 ...(iii)1<2(1−a)2<3⇒ −2<a<0 ...(iv)From(i),(ii),(iii) and (iv)...∴ aϵ(−87, −1]