If the roots of the equation `x^2-8x+a^2-6a=0` are real distinct, then find all possible value of `adot`

Explanation

Since the roots of the given equation are real and distinct, we must have
`D gt 0`
`rArr 64 - 4 (a^(2) - 6a) gt 0`
or ` 4[16 - a^(2) + 6a] gt 0`
or `-4 (a^(2) - 6a - 16 gt 0`
or `a^(2) - 6a - 16 lt 0`
or `(a - 8)(a +2) lt 0`
`rArr - 2 lt a lt 8`
Hence, the roots of the given equation are real if a lies between - 2 and 8