All possible values of a, so that 6 lies between the roots of the equation `x^2 + 2(a-3)x +9 =0`

Explanation

Let `f(x)=x^(2)+2(p-3)x+9`, as 6 lies between the roots of `f(x)=0`, we can take `Dgt0` and `afd(6)lt0`
(i) Consider `Dgt0`

`{2(p-3)}^(2)-4.1.9gt0`
`implies(p-3)^(2)-9gt0`
`impliesp(p-6)gt0`
`impliesp epsilon(-oo,0)uu(6,oo)`............i
(ii) Consider `afd(6)lt0`
`1.{36+12(p-3)+9}lt0`
`implies12p+9lt0impliesp+3/4lt0`
`rarrp epsilon(-oo,-3/4)`...........ii
Hence the values of `p` satisfying Eqs (i) and (ii) at the same time are `p epsilon(-oo,-3/4)`.