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Question

If x2 + 2(a - 1)x + a + 5 =0 has real roots belonging to the interval (1, 3) then aϵ


A

(, 87]

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B

(4, )

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C

(, 483)

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D

(87, 1)

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Solution

The correct option is D

(87, 1)


x2 + 2 (a - 1)x + a + 5 = 0 has roots ϵ (1, 3)
Δ0, f(1)>0, f(3)>0, 1<B2A<3 4(a1)24(a+5)0 (1+a)(a4)0aϵ(, 1][4, ) ...(i)1+2(a1)+a+5>0 a>43 ...(ii)9+2(91)3+a+5>0 a>87 ...(iii)1<2(1a)2<3 2<a<0 ...(iv)From(i),(ii),(iii) and (iv)... aϵ(87, 1]


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