Find the values of a if `x^2-2(a-1)x+(2a+1)=0` has positive roots.

Explanation

Let `f(x) = x^(2) - 2 (a - 1) x + (2a + 1) ` . Then f(x) = 0 will have both
roots positive , if
` (i) D gt 0 `
`rArr 4(a - 1)^(2) - 4 (2a + 1) ge 0 `
`rArr a^(2) - 4a ge 0 `
`rArr a le or a ge 4 ` (1)
(ii) Sum of the roots `gt `0
`rArr 2(a - 1) gt rArr a gt 1` (2)
(iii) Product of roots `gt` 0
` rArr (2a + 1) gt 0 rArr a gt - (1)/(2)` (3)
From (1), (2), and (3), we get a `ge` 4 .