AMU Engineering 2018 solved paper Solved Paper

If both roots of the equation
x2−2(a−1)x+(2a+1)=0 are positive.
Then following conditions must be true(i) D≥0
(ii) 2(a−1)>0
(iii) 2a+1>0
Case I D=(−2(a−1))2−4(2a+1)≥0
4(a2−2a+1)−4(2a+1)≥0
a2−4a≥0
a(a−4)≥0
a∈(−∞,0]∪[4,∞) .........(i)
Case II 2(a−1)>0
a>1
a∈(1,∞) ........(ii)
Case III 2a+1>0
a>

−1

2

.........(iii)
From Eqs. (i), (ii) and (iii),
we get, a∈[4,∞)