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Q.

Let S denote the set of all real values of a for which the roots of the equation x22ax+a21=0     

lie between 5 and 10, then S equals

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a

(– 1, 2)

b

(4, 9)

c

(6, 9)

d

(2, 9)

answer is D.

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Detailed Solution

We can write (1) as

(xa)2=1x=a±1

Now, 5<a±1<10

    4<a<9,6<a<11    a(6,9).

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Let S denote the set of all real values of a for which the roots of the equation x2−2ax+a2−1=0     lie between 5 and 10, then S equals