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If both the roots of x^2+a x+2=0 lies in...

If both the roots of `x^2+a x+2=0` lies in the interval (0, 3), then find the exhaustive range of value of `adot`

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Both roots of `x^(2) + ax + 2 = 0 ` lies in the interval (0,3). Compare
this equation with `Ax^(2) x + Bx + C = 0` . Then , the required conditions are
(i) `D = a^(2) - 8 ge 0 rArr a in (-infty, - 2 sqrt(2)] cap [2sqrt(2), infty)` (1)
(ii) `Af (0) gt 0 and Af (3) gt 0 `
`rArr 2 gt 0, 9 + 3a + 2 gt 0 `
`rArr a in (- (11)/(3), infty)` (2)
`(iii) 0 lt - (B)/(2A) lt 3`
`rArr 0 lt - (a)/(2) lt3`
`rArr - 6 lt a lt 0 ` (3)
From (1), (2) and (3) , ` a in (-11/ 3 , - 2 sqrt(2)]` .
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