If both the roots of `a x^2+a x+1=0` are less than 1, then find the exhaustive range of values of `adot`

Explanation

Both roots of `ax^(2) + ax + 1 = 0` are less then 1 . Compare this
equation with `Ax^(2) + Bx + C = 0` . Then, the required conditions are
(i) ` D = a^(2) - 4a ge 0 rArr a in (-infty, 0 ]cap [4, infty)` (1)
(ii) `- (B)/(2A) gt 1 rArr - (a)/(2a)lt 1 ` (which is always true as a `ne`0)
(iii) ` Af(1) gt 0 `
`rArr a(2a + 1) gt 0`
`rArr ain (-infty,-(1)/(2)) cap (0, infty).` (2)
From (1) and (2) , `a in (-infty, - 1//2) cap [4, infty)` .