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Question

The set of values of a for which the sum and product of roots of the equation x2(a25a+5)x+(2a23a4)=0 is less than 1, is

A
(1,52)
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B
(1,4)
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C
(1,52)
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D
(1,4)
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Solution

The correct option is C (1,52)
Given equation
x2(a25a+5)x+(2a23a4)=0
Let the roots of the equation be m,n.
So, m+n<1,mn<1

m+n<1
a25a+5<1a25a+4<0(a4)(a1)<0a(1,4) (1)

mn<1
2a23a4<12a23a5<0(a+1)(2a5)<0a(1,52) (2)

From (1) and (2),
a(1,52)

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