`4 x^2-2 x+a=0,` has one roots then find the value of a ?

Explanation

Let `f(x)=4x^(2)-2x+a` as both roots of the equation `f(x)=0` are lie between `(-1,1)` we can take `D ge0`
`af(-1)gt0,af(1)gt0` and `-1lt1/4lt1`
(i) Consider `Dge0`
`(-2)^(2)-4.4.age0impliesale1/4`…….i
(ii) Consider `af(-1)gt0`
`4(4+2+a)gt0`
`impliesage-6impliesa epsilon(-6,oo)`.............ii
(iii) Consider `af(1)gt0`
`4(4-2+a)gt0impliesagt-2`
`impliesa epsilon(-2,oo)`.........iii
Hence the values of `a` satisfying Eqs. (i), (ii) and (iii) at the same time are `a epsilon(-2,1/4]`