Q.

The least integral value of ‘a’ for which the equation x2−2(a−1) x +(2a+1)=0 has both the roots positive is

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a

3

b

4

c

1

d

5

answer is B.

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Detailed Solution

If two roots are positive  a,b are of different sign and △⩾0 Δ≥0 and coeff of x<0 ⇒4(a−1)2−4(2a+1)≥0 ;               −2(a−1)<0⇒a2−4a≥0                                          ⇒a−1>0    a≤0 or a≥4                                                ⇒a>1
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The least integral value of ‘a’ for which the equation x2−2(a−1) x +(2a+1)=0 has both the roots positive is