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Question

The least positive integral value of m for which the equation x22(m1)x+2m+1=0 has both roots positive is

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Solution

x22(m1)x+2m+1=0
Since, both roots are positive, then required condions are

(i) D0(m1)2(2m+1)0
m(,0][4,)

(ii) ba>0m>1

(iii) ca>0m>12

(i)(ii)(iii)m4
So, least positive integer is 4.

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