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Question

If the roots of x2 - (a - 3)x + a = 0 are such that at least one of the root is greater than 2, then find the range of a.


A

[7, 9]

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B

[7, )

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C

[9, )

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D

(7, 9)

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Solution

The correct option is C

[9, )


x2 - (a - 3)x + a = 0
D= (a3)2 - 4a = a2 - 10a + 9 = (a - 1)(a - 9)
Case 1: Both roots are greater than 2
(i) D0 (a1)(a9)0 a(, 1][9, )
(ii) f(2)>04(a3)2+a>0 a<10
(iii) b2a>2a32>2a>7
a [9, 10)
Case 2 :- One root is greater than 2 and other is less than or equal to 2
(i) D0 (a1)(a9)0 a(,1][9, )
(ii) f(2)0 4(a3)2+a0 a10
a[10, )
So from both the cases we get, a[9, )


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